Journal articles: 'Solution's accuracy'

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Bae, Tae-Suk, Dorota Grejner-Brzezinska, and Jay Hyoun Kwon. "Efficient LEO Dynamic Orbit Determination with Triple Differenced GPS Carrier Phases." Journal of Navigation 60, no. 2 (April 20, 2007): 217–32. http://dx.doi.org/10.1017/s0373463307004171.

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The dynamic precise orbit determination of a Low Earth Orbit satellite using triple differenced GPS phases is presented in this study. The atmospheric drag parameters are estimated to compensate the incomplete atmosphere model for better precision of the orbit solution. In addition, the empirical force parameters, especially once- and twice-per-revolution components, along with the new IERS Conventions and models to compute the perturbing forces are introduced to absorb the remaining unmodelled forces. The optimal arc length for the parameterization and the data processing strategy are also tested and analyzed for the best orbit solutions. The triple differencing technique enables fast and efficient orbit estimation, because no ambiguity resolution and cycle slip detection are required. With the triple differenced ion-free GPS phase observables, the orbit and the velocity solutions for 24 hours of CHAMP are calculated; they compare with the published Rapid Science Orbit with the accuracy of 8 cm and 0·12 mm/s in 3D RMS for the orbit and the velocity, respectively, and are statistically consistent with the RSO when it is not better than 4 cm in terms of an absolute accuracy. The approach presented here provides an efficient and simple, but robust, alternative approach, while the solution's accuracy is still comparable to the double-difference results.

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Rojas, Camilo, Niels Poulsen, Mileva Van Tuyl, Daniel Vargas, Zipporah Cohen, Joe Paradiso, Pattie Maes, Kevin Esvelt, and Fadel Adib. "A Scalable Solution for Signaling Face Touches to Reduce the Spread of Surface-based Pathogens." Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies 5, no. 1 (March 19, 2021): 1–22. http://dx.doi.org/10.1145/3448121.

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Hand-to-Face transmission has been estimated to be a minority, yet non-negligible, vector of COVID-19 transmission and a major vector for multiple other pathogens. At the same time, as it cannot be effectively addressed with mainstream protection measures, such as wearing masks or tracing contacts, it remains largely untackled. To help address this issue, we have developed Saving Face - an app that alerts users when they are about to touch their faces, by analyzing the distortion patterns in the ultrasound signal emitted by their earphones. The system only relies on pre-existing hardware (a smartphone with generic earphones), which allows it to be rapidly scalable to billions of smartphone users worldwide. This paper describes the design, implementation and evaluation of the system, as well as the results of a user study testing the solution's accuracy, robustness, and user experience during various day-to-day activities (93.7% Sensitivity and 91.5% Precision, N=10). While this paper focuses on the system's application to detecting hand-to-face gestures, the technique can also be applicable to other types of gestures and gesture-based applications.

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Aeffner, Famke, Kristin Wilson, Nathan T. Martin, Joshua C. Black, Cris L. Luengo Hendriks, Brad Bolon, Daniel G. Rudmann, et al. "The Gold Standard Paradox in Digital Image Analysis: Manual Versus Automated Scoring as Ground Truth." Archives of Pathology & Laboratory Medicine 141, no. 9 (May 30, 2017): 1267–75. http://dx.doi.org/10.5858/arpa.2016-0386-ra.

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Context.— Novel therapeutics often target complex cellular mechanisms. Increasingly, quantitative methods like digital tissue image analysis (tIA) are required to evaluate correspondingly complex biomarkers to elucidate subtle phenotypes that can inform treatment decisions with these targeted therapies. These tIA systems need a gold standard, or reference method, to establish analytical validity. Conventional, subjective histopathologic scores assigned by an experienced pathologist are the gold standard in anatomic pathology and are an attractive reference method. The pathologist's score can establish the ground truth to assess a tIA solution's analytical performance. The paradox of this validation strategy, however, is that tIA is often used to assist pathologists to score complex biomarkers because it is more objective and reproducible than manual evaluation alone by overcoming known biases in a human's visual evaluation of tissue, and because it can generate endpoints that cannot be generated by a human observer. Objective.— To discuss common visual and cognitive traps known in traditional pathology-based scoring paradigms that may impact characterization of tIA-assisted scoring accuracy, sensitivity, and specificity. Data Sources.— This manuscript reviews the current literature from the past decades available for traditional subjective pathology scoring paradigms and known cognitive and visual traps relevant to these scoring paradigms. Conclusions.— Awareness of the gold standard paradox is necessary when using traditional pathologist scores to analytically validate a tIA tool because image analysis is used specifically to overcome known sources of bias in visual assessment of tissue sections.

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WU, S. C., H. O. ZHANG, C. ZHENG, and J. H. ZHANG. "A HIGH PERFORMANCE LARGE SPARSE SYMMETRIC SOLVER FOR THE MESHFREE GALERKIN METHOD." International Journal of Computational Methods 05, no. 04 (December 2008): 533–50. http://dx.doi.org/10.1142/s0219876208001613.

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One main disadvantage of meshfree methods is that their memory requirement and computational cost are much higher than those of the usual finite element method (FEM). This paper presents an efficient and reliable solver for the large sparse symmetric positive definite (SPD) system resulting from the element-free Galerkin (EFG) approach. A compact mathematical model of heat transfer problems is first established using the EFG procedure. Based on the widely used Successive Over-Relaxation–Preconditioned Conjugate Gradient (SSOR–PCG) scheme, a novel solver named FastPCG is then proposed for solving the SPD linear system. To decrease the computational time in each iteration step, a new algorithm for realizing multiplication of the global stiffness matrix by a vector is presented for this solver. The global matrix and load vector are changed in accordance with a special rule and, in this way, a large account of calculation is avoided on the premise of not decreasing the solution's accuracy. In addition, a double data structure is designed to tackle frequent and unexpected operations of adding or removing nodes in problems of dynamic adaptive or moving high-gradient field analysis. An information matrix is also built to avoid drastic transformation of the coefficient matrix caused by the initial-boundary values. Numerical results show that the memory requirement of the FastPCG solver is only one-third of that of the well-developed AGGJE solver, and the computational cost is comparable with the traditional method with the increas of solution scale and order.

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Wee, Tae-Kwon. "A variational regularization of Abel transform for GPS radio occultation." Atmospheric Measurement Techniques 11, no. 4 (April 6, 2018): 1947–69. http://dx.doi.org/10.5194/amt-11-1947-2018.

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Abstract. In the Global Positioning System (GPS) radio occultation (RO) technique, the inverse Abel transform of measured bending angle (Abel inversion, hereafter AI) is the standard means of deriving the refractivity. While concise and straightforward to apply, the AI accumulates and propagates the measurement error downward. The measurement error propagation is detrimental to the refractivity in lower altitudes. In particular, it builds up negative refractivity bias in the tropical lower troposphere. An alternative to AI is the numerical inversion of the forward Abel transform, which does not incur the integration of error-possessing measurement and thus precludes the error propagation. The variational regularization (VR) proposed in this study approximates the inversion of the forward Abel transform by an optimization problem in which the regularized solution describes the measurement as closely as possible within the measurement's considered accuracy. The optimization problem is then solved iteratively by means of the adjoint technique. VR is formulated with error covariance matrices, which permit a rigorous incorporation of prior information on measurement error characteristics and the solution's desired behavior into the regularization. VR holds the control variable in the measurement space to take advantage of the posterior height determination and to negate the measurement error due to the mismodeling of the refractional radius. The advantages of having the solution and the measurement in the same space are elaborated using a purposely corrupted synthetic sounding with a known true solution. The competency of VR relative to AI is validated with a large number of actual RO soundings. The comparison to nearby radiosonde observations shows that VR attains considerably smaller random and systematic errors compared to AI. A noteworthy finding is that in the heights and areas that the measurement bias is supposedly small, VR follows AI very closely in the mean refractivity deserting the first guess. In the lowest few kilometers that AI produces large negative refractivity bias, VR reduces the refractivity bias substantially with the aid of the background, which in this study is the operational forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF). It is concluded based on the results presented in this study that VR offers a definite advantage over AI in the quality of refractivity.

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NAKAMURA, Susumu, and Masaaki KUBOTA. "Accuracy of pH standard solutions." Bunseki kagaku 36, no. 5 (1987): T58—T60. http://dx.doi.org/10.2116/bunsekikagaku.36.5_t58.

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FLOURI, EVANGELIA T., JOHN A. EKATERINARIS, and NIKOLAOS A. KAMPANIS. "HIGH-ORDER ACCURATE NUMERICAL SCHEMES FOR THE PARABOLIC EQUATION." Journal of Computational Acoustics 13, no. 04 (December 2005): 613–39. http://dx.doi.org/10.1142/s0218396x05002888.

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Efficient, high-order accurate methods for the numerical solution of the standard (narrow-angle) parabolic equation for underwater sound propagation are developed. Explicit and implicit numerical schemes, which are second- or higher-order accurate in time-like marching and fourth-order accurate in the space-like direction are presented. The explicit schemes have severe stability limitations and some of the proposed high-order accurate implicit methods were found conditionally stable. The efficiency and accuracy of various numerical methods are evaluated for Cartesian-type meshes. The standard parabolic equation is transformed to body fitted curvilinear coordinates. An unconditionally stable, implicit finite-difference scheme is used for numerical solutions in complex domains with deformed meshes. Simple boundary conditions are used and the accuracy of the numerical solutions is evaluated by comparing with an exact solution. Numerical solutions in complex domains obtained with a finite element method show excellent agreement with results obtained with the proposed finite difference methods.

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Arefin, Mohammad Asif, Biswajit Gain, and Rezaul Karim. "Accuracy Analysis on Solution of Initial Value Problems of Ordinary Differential Equations for Some Numerical Methods with Different Step Sizes." International Annals of Science 10, no. 1 (March 7, 2021): 118–33. http://dx.doi.org/10.21467/ias.10.1.118-133.

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In this article, three numerical methods namely Euler’s, Modified Euler, and Runge-Kutta method have been discussed, to solve the initial value problem of ordinary differential equations. The main goal of this research paper is to find out the accurate results of the initial value problem (IVP) of ordinary differential equations (ODE) by applying the proposed methods. To achieve this goal, solutions of some IVPs of ODEs have been done with the different step sizes by using the proposed three methods, and solutions for each step size are analyzed very sharply. To ensure the accuracy of the proposed methods and to determine the accurate results, numerical solutions are compared with the exact solutions. It is observed that numerical solutions are best fitted with exact solutions when the taken step size is very much small. Consequently, all the proposed three methods are quite efficient and accurate for solving the IVPs of ODEs. Error estimation plays a significant role in the establishment of a comparison among the proposed three methods. On the subject of accuracy and efficiency, comparison is successfully implemented among the proposed three methods.

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Haji-Sheikh, A., and J. V. Beck. "Green’s Function Partitioning in Galerkin-Based Integral Solution of the Diffusion Equation." Journal of Heat Transfer 112, no. 1 (February 1, 1990): 28–34. http://dx.doi.org/10.1115/1.2910360.

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A procedure to obtain accurate solutions for many transient conduction problems in complex geometries using a Galerkin-based integral (GBI) method is presented. The nonhomogeneous boundary conditions are accommodated by the Green’s function solution technique. A Green’s function obtained by the GBI method exhibits excellent large-time accuracy. It is shown that the time partitioning of the Green’s function yields accurate small-time and large-time solutions. In one example, a hollow cylinder with convective inner surface and prescribed heat flux at the outer surface is considered. Only a few terms for both large-time and small-time solutions are sufficient to produce results with excellent accuracy. The methodology used for homogeneous solids is modified for application to complex heterogeneous solids.

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Wang, Xiao Dan, and Guang Yu Shi. "Evaluation of Various Laminated Plate Theories Accounting for Interlaminar Transverse Shear Stress Continuity." Advanced Materials Research 716 (July 2013): 119–26. http://dx.doi.org/10.4028/www.scientific.net/amr.716.119.

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Based on a unified form of the plate kinematics in terms of the transverse shear functions and the Heaviside step function, the analytical solutions of laminated plates corresponding to a number of higher-order shear deformation plate theories are solved in this paper. The accuracy assessment of these higher-order laminated plate theories is conducted by comparing the resulting analytical solutions with the elasticity solutions and finite element results. The accuracy study shows that the interlaminar shear stress continuity condition is very important for the accurate prediction of the transverse shear stresses across the laminated plate thickness. The comparison study also indicates that the new laminated plate theory accounting for the interlaminar transverse shear stress continuity proposed by the authors yields both very accurate displacements and accurate stresses. This new higher-order laminated plate theory can be efficiently used in the finite element analysis of laminated composite plates since it uses the same five field variables as those used in the first-order shear deformation plate theory.

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VALENCIANO, J., and M. A. J. CHAPLAIN. "COMPUTING HIGHLY ACCURATE SOLUTIONS OF A TUMOUR ANGIOGENESIS MODEL." Mathematical Models and Methods in Applied Sciences 13, no. 05 (May 2003): 747–66. http://dx.doi.org/10.1142/s0218202503002702.

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In this paper we describe and implement a numerical method which provides highly accurate solutions of a generic two-dimensional model for the formation of capillary networks as a partial process in tumour angiogenesis. The model includes effects due to diffusion, chemotaxis, haptotaxis and cell proliferation. The governing partial differential equation is a diffusion-advection-reaction equation of parabolic type. In order to achieve high accuracy in space, we use a semi-discretisation based on the spectral element method. The resulting system of stiff ordinary differential equations is advanced forward in time using one-step explicit higher order time integrators based on Taylor series expansions. The high accuracy in space is monitored by a residual based a posteriori error indicator while the high accuracy in time is guaranteed by the local and global truncation errors of the higher order Taylor series method.

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Yao, Zhonghua, Gang Li, and Jinmei Gao. "A High Order Well-Balanced Finite Volume WENO Scheme for a Blood Flow Model in Arteries." East Asian Journal on Applied Mathematics 7, no. 4 (November 2017): 852–66. http://dx.doi.org/10.4208/eajam.181016.300517f.

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AbstractThe numerical simulations for the blood flow in arteries by high order accurate schemes have a wide range of applications in medical engineering. The blood flow model admits the steady state solutions, in which the flux gradient is non-zero and is exactly balanced by the source term. In this paper, we present a high order finite volume weighted essentially non-oscillatory (WENO) scheme, which preserves the steady state solutions and maintains genuine high order accuracy for general solutions. The well-balanced property is obtained by a novel source term reformulation and discretisation, combined with well-balanced numerical fluxes. Extensive numerical experiments are carried out to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

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de Menezes, L. R. A. X., and W. J. R. Hoefer. "Accuracy of TLM solutions of Maxwell's equations." IEEE Transactions on Microwave Theory and Techniques 44, no. 12 (1996): 2512–18. http://dx.doi.org/10.1109/22.554589.

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Higham, Nicholas J. "The Accuracy of Solutions to Triangular Systems." SIAM Journal on Numerical Analysis 26, no. 5 (October 1989): 1252–65. http://dx.doi.org/10.1137/0726070.

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Earle, Michael A. "Accurate Harmonic Series for Inverse and Direct Solutions for the Great Ellipse." Journal of Navigation 64, no. 3 (June 7, 2011): 557–70. http://dx.doi.org/10.1017/s037346331100004x.

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In this paper, formulae drawn from the discipline of map projections are applied to provide simple and accurate solutions for the Inverse and Direct problems on the Great Ellipse. Distance along the meridional arc of the spheroid as a function of geodetic latitude is defined in terms of an elliptic integral which will be replaced here with a compact harmonic series approximation possessing simplicity and high accuracy. Latitude as a function of distance along the meridional arc will also be obtained via another equally simple inversion series that also possesses high accuracy. When these two series are applied with their constants modified to suit the section ellipse, they will be shown to provide accurate solutions to the inverse and direct navigation problems pertaining to the Great Ellipse, and thereby provide a complete solution that is also simple to implement.

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Dolan, J. P., and W. S. Worley. "Closed-Form Approximations to the Solution of V-Belt Force and Slip Equations." Journal of Mechanisms, Transmissions, and Automation in Design 107, no. 2 (June 1, 1985): 292–300. http://dx.doi.org/10.1115/1.3258723.

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A method for generating accurate numerical solutions of the exact differential equations describing tension distribution and radial penetration of a flexible V-belt on driveN and driveR sheaves is presented and results are compared with approximate solutions reported in the literature. Analytical approximations for these solutions of higher accuracy than any previously published have been found and are presented. They suggest important modifications of current design practice for belt tensioning and life appraisal.

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Fielitz, P., and Günter Borchardt. "Approximate Solutions of Grain Boundary Diffusion in Thin Films in the B₂ Regime." Defect and Diffusion Forum 237-240 (April 2005): 206–11. http://dx.doi.org/10.4028/www.scientific.net/ddf.237-240.206.

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Exact mathematical solutions of the grain boundary diffusion equation in thin films have generally a complicated form, which is too cumbersome for the evaluation of experimental average concentration depth profiles obtained by sectioning techniques. On the other hand the accuracy of the exact solutions is not necessary for practical purposes so that it is useful to derive sufficiently accurate approximate solutions. We propose a method to derive such solutions for a thin film if the grain boundary diffusion is in the B2 regime. These solutions are derived for different diffusion sources.

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Allahyari, Majid, Vahid Esfahanian, and Kianoosh Yousefi. "The Effects of Grid Accuracy on Flow Simulations: A Numerical Assessment." Fluids 5, no. 3 (July 10, 2020): 110. http://dx.doi.org/10.3390/fluids5030110.

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High-quality, accurate grid generation is a critical challenge in the computational simulation of fluid flows around complex geometries. In particular, the accuracy of the grids is an effective factor in order to achieve a successful numerical simulation. In the current study, we present a series of systematic numerical simulations for fluid flows around a NACA 0012 airfoil using different computational grid generation techniques, including the standard second-order, fourth-order compact, and Theodorsen transformation approaches, to assess the effects of grid accuracy on the flow solutions. The flow solvers are based on the second- and fourth-order schemes for spatial discretizations and Beam-Warming linearization method for time advancement. The obtained grids, as well as the metrics and the corresponding numerical flow solution for each grid generation technique, are compared and studied in detail. It is demonstrated that the quality and orthogonality of the grids is improved by using the fourth-order compact scheme. Moreover, the numerical assessment showed that the accuracy and the quality of the grids directly influence the numerical flow solutions. Finally, the higher-order accurate flow solvers are found to be more sensitive to the accuracy of the generated grid.

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Vu, L. G., Abeer Alsadoon, P. W. C. Prasad, and A. M. S. Rahma. "Improving Accuracy in Face Recognition Proposal to Create a Hybrid Photo Indexing Algorithm, Consisting of Principal Component Analysis and a Triangular Algorithm (PCAaTA)." International Journal of Pattern Recognition and Artificial Intelligence 31, no. 01 (January 2017): 1756001. http://dx.doi.org/10.1142/s0218001417560018.

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Accurate face recognition is today vital, principally for reasons of security. Current methods employ algorithms that index (classify) important features of human faces. There are many current studies in this field but most current solutions have significant limitations. Principal Component Analysis (PCA) is one of the best facial recognition algorithms. However, there are some noises that could affect the accuracy of this algorithm. The PCA works well with the support of preprocessing steps such as illumination reduction, background removal and color conversion. Some current solutions have shown results when using a combination of PCA and preprocessing steps. This paper proposes a hybrid solution in face recognition using PCA as the main algorithm with the support of a triangular algorithm in face normalization in order to enhance indexing accuracy. To evaluate the accuracy of the proposed hybrid indexing algorithm, the PCAaTA is tested and the results are compared with current solutions.

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LUO, WENYU, RENHE ZHANG, and HENRIK SCHMIDT. "AN EFFICIENT AND NUMERICALLY STABLE COUPLED-MODE SOLUTION FOR RANGE-DEPENDENT PROPAGATION." Journal of Computational Acoustics 20, no. 03 (September 2012): 1250008. http://dx.doi.org/10.1142/s0218396x12500087.

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An efficient and numerically stable coupled-mode solution is presented for acoustic propagation in a range-dependent waveguide. This model is numerically stable due to the appropriately normalized range solutions introduced in the formulation. In addition, by combining a forward marching and a backward marching, this model provides accurate solutions for range-dependent waveguides characterized by large bottom slope angles and/or high impedance contrast. Besides high accuracy, this two-way solution also provides high efficiency, which is achieved by applying the single-scatter approximation. Numerical examples are also provided to demonstrate the stability, accuracy, and efficiency of this model.

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Fu, Sonia, Pierre Jacolot, Tommaso Balercia, Christian Rom, Jørgen B. Andersen, and Gert F. Pedersen. "On the Accuracy of Asymptotic Solutions for TM Waves Diffracting on an Impedance Wedge." International Journal of Antennas and Propagation 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/695670.

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The contribution focuses on the accuracy of two asymptotic solutions aimed at representing the electromagnetic field scattered by penetrable wedges. One is a heuristic manipulation of the solution for the perfect electrical conductor, and the other one is a more rigorous coefficient based on approximate boundary conditions. The results presented here extend those proposed by other authors by illustrating the accuracy of such solutions at the edge of validity of the uniform theory of diffraction. In particular, they show that the heuristic formulation can be freely applied in similar conditions, while the other might not always lead to accurate predictions.

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Gurarslan, Gurhan. "Sixth-Order Combined Compact Finite Difference Scheme for the Numerical Solution of One-Dimensional Advection-Diffusion Equation with Variable Parameters." Mathematics 9, no. 9 (May 1, 2021): 1027. http://dx.doi.org/10.3390/math9091027.

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A high-accuracy numerical method based on a sixth-order combined compact difference scheme and the method of lines approach is proposed for the advection–diffusion transport equation with variable parameters. In this approach, the partial differential equation representing the advection-diffusion equation is converted into many ordinary differential equations. These time-dependent ordinary differential equations are then solved using an explicit fourth order Runge–Kutta method. Three test problems are studied to demonstrate the accuracy of the present methods. Numerical solutions obtained by the proposed method are compared with the analytical solutions and the available numerical solutions given in the literature. In addition to requiring less CPU time, the proposed method produces more accurate and more stable results than the numerical methods given in the literature.

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Neagoe, Mircea, Ion Visa, Nadia Cretescu, and Macedon Moldovan. "On a New Parallel Tracking System for Accurate Orientation of Concentrated Solar Convertors." Applied Mechanics and Materials 658 (October 2014): 105–10. http://dx.doi.org/10.4028/www.scientific.net/amm.658.105.

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The concentrated solar energy convertors (e.g. solar-thermal dish, concentrated photovoltaic) require high tracking accuracy to maintain low incidence angles of the solar ray in relation with the concentrator optical axis (e.g. tracking accuracy of 0.05°...0.1°). This functional requirement is currently ensured by the high performance dual-axis solar tracking systems, able to reach the imposed accuracy, including expensive rotary actuator solutions. This paper proposes a new high accuracy tracking system for diurnal orientation, integrating a 2 DOF parallel linkage driven by linear actuators, as a simple, accurate, and cost-effective solution. A kinematic and static approach used for optimisation of the driving programs of the two linear actuators is presented, following the requirements: a) ensure the imposed tracking accuracy and b) achieve advantageous transmitting angles and hence lowest driving forces. The performances of the system are analysed on large orientation strokes (over 130°); the results obtained confirm the viability of the new tracking system concept, with higher performances compared to other similar known solutions.

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Bougoffa, Lazhar, and Abdul-Majid Wazwaz. "New approximate solutions of the Blasius equation." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 7 (September 7, 2015): 1590–99. http://dx.doi.org/10.1108/hff-08-2014-0263.

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Purpose – The purpose of this paper is to propose a reliable treatment for studying the Blasius equation, which arises in certain boundary layer problems in the fluid dynamics. The authors propose an algorithm of two steps that will introduce an exact solution to the equation, followed by a correction to that solution. An approximate analytic solution, which contains an auxiliary parameter, is obtained. A highly accurate approximate solution of Blasius equation is also provided by adding a third initial condition y ' ' (0) which demonstrates to be quite accurate by comparison with Howarth solutions. Design/methodology/approach – The approach consists of two steps. The first one is an assumption for an exact solution that satisfies the Blasius equation, but does not satisfy the given conditions. The second step depends mainly on using this assumption combined with the given conditions to derive an accurate approximation that improves the accuracy level. Findings – The obtained approximation shows an enhancement over some of the existing techniques. Comparing the calculated approximations confirm the enhancement that the derived approximation presents. Originality/value – In this work, a new approximate analytical solution of the Blasius problem is obtained, which demonstrates to be quite accurate by comparison with Howarth solutions.

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Gluzman, S., and V. I. Yukalov. "Self-similarly corrected Padé approximants for nonlinear equations." International Journal of Modern Physics B 33, no. 29 (November 20, 2019): 1950353. http://dx.doi.org/10.1142/s0217979219503533.

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We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Padé approximants that are known to provide the best approximation for the class of rational functions, but do not provide sufficient accuracy or cannot be applied at all for those nonlinear problems, whose solutions exhibit behavior characterized by irrational functions. In order to improve the accuracy, we suggest a method of self-similarly corrected Padé approximants taking into account the irrational functional behavior. The idea of the method is in representing the sought solution as a product of two factors, one of which is given by a self-similar root approximant, responsible for irrational functional behavior, and the other being a Padé approximant corresponding to a rational function. The efficiency of the method is illustrated by constructing very accurate solutions for nonlinear differential equations. A thorough investigation is given proving that the suggested method is more accurate than the method of standard Padé approximants.

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Sari, Murat. "Solution of the Porous Media Equation by a Compact Finite Difference Method." Mathematical Problems in Engineering 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/912541.

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Accurate solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer and in biological systems are obtained using a compact finite difference method in space and a low-storage total variation diminishing third-order Runge-Kutta scheme in time. In the calculation of the numerical derivatives, only a tridiagonal band matrix algorithm is encountered. Therefore, this scheme causes to less accumulation of numerical errors and less use of storage space. The computed results obtained by this way have been compared with the exact solutions to show the accuracy of the method. The approximate solutions to the equation have been computed without transforming the equation and without using linearization. Comparisons indicate that there is a very good agreement between the numerical solutions and the exact solutions in terms of accuracy. This method is seen to be a very good alternative method to some existing techniques for such realistic problems.

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Samsudin, Nooraida, Nurhafizah Moziyana Mohd Yusop, Syahrul Fahmy, and Anis Shahida Niza Binti Mokhtar. "Cube Arithmetic: Improving Euler Method for Ordinary Differential Equation using Cube Mean." Indonesian Journal of Electrical Engineering and Computer Science 11, no. 3 (September 1, 2018): 1109. http://dx.doi.org/10.11591/ijeecs.v11.i3.pp1109-1113.

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The Euler method is a first-order numerical procedure for solving Ordinary Differential Equation (ODEs) problems. It is an effective and easy method to solve initial value problems. Although Euler provides simple procedure for solving ODEs, there have been issues such as complexity, time of processing and accuracy that compelled the use of other, more complex, methods. Improvements to the Euler method have attracted much attention resulting in numerous modified Euler methods. This paper proposes Cube Arithmetic, a modified Euler method with improved accuracy. The efficiency of Cube Arithmetic was compared with Euler Arithmetic and tested using SCILAB against exact solutions. Results indicate that not only Cube Arithmetic provided solutions that are similar to exact solutions at small step size, but also at higher step size, hence producing more accurate results.

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Alfianti, Zulia Imami, Deni Gunawan, and Ahmad Fikri Amin. "SENTIMENT ANALYSIS OF COSMETIC REVIEW USING NAIVE BAYES AND SUPPORT VECTOR MACHINE METHOD BASED ON PARTICLE SWARM OPTIMIZATION." Jurnal Riset Informatika 2, no. 3 (June 22, 2020): 169–78. http://dx.doi.org/10.34288/jri.v2i3.149.

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Sentiment analysis is an area of approach that solves problems by using reviews from various relevant scientific perspectives. Reading a review before buying a product is very important to know the advantages and disadvantages of the products we will use, besides reading a cosmetic review can find out the quality of the cosmetic brand is feasible or not be used. Before consumers decide to buy cosmetics, consumers should know in detail the products to be purchased, this can be learned from the testimonials or the results of reviews from consumers who have bought and used the previous product. The number of reviews is certainly very much making consumers reluctant to read reviews. Eventually, the reviews become useless. For this reason, the authors classify based on positive and negative classes, so consumers can find product comparisons quickly and precisely. The implementation of Particle Swarm Optimization (PSO) optimization can improve the accuracy of the Support Vector Machine (SVM) and Naïve Bayes (NB) algorithm can improve accuracy and provide solutions to the review classification problem to be more accurate and optimal. Comparison of accuracy resulting from testing this data is an SVM algorithm of 89.20% and AUC of 0.973, then compared to SVM based on PSO with an accuracy of 94.60% and AUC of 0.985. The results of testing the data for the NB algorithm are 88.50% accuracy and AUC is 0.536, then the accuracy is compared with the PSO based NB for 0.692. In these calculations prove that the application of PSO optimization can improve accuracy and provide more accurate and optimal solutions

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Karlin, V., V. Maz’ya, and G. Schmidt. "High accuracy periodic solutions to the Sivashinsky equation." Journal of Computational Physics 188, no. 1 (June 2003): 209–31. http://dx.doi.org/10.1016/s0021-9991(03)00164-5.

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Turner, Kathryn, and Homer F. Walker. "Efficient High Accuracy Solutions with ${\text{GMRES}}(m)$." SIAM Journal on Scientific and Statistical Computing 13, no. 3 (May 1992): 815–25. http://dx.doi.org/10.1137/0913048.

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Jasti, J. K., V. R. Penmatcha, and D. K. Babu. "Use of Analytical Solutions To Improve Simulator Accuracy." SPE Journal 4, no. 01 (March 1, 1999): 47–56. http://dx.doi.org/10.2118/55225-pa.

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Kozmann, G., G. Tuboly, I. Maros, D. Wei, and X. Zhu. "Accuracy of electrocardiological inverse solutions: a model study." Journal of Electrocardiology 46, no. 4 (July 2013): e16. http://dx.doi.org/10.1016/j.jelectrocard.2013.05.059.

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Gupta, Murli M. "High accuracy solutions of incompressible Navier-Stokes equations." Journal of Computational Physics 89, no. 2 (August 1990): 488–89. http://dx.doi.org/10.1016/0021-9991(90)90157-v.

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Gupta, Murli M. "High accuracy solutions of incompressible Navier-Stokes equations." Journal of Computational Physics 93, no. 2 (April 1991): 343–59. http://dx.doi.org/10.1016/0021-9991(91)90188-q.

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Koçak, Mustafa Murat, Sibel Koçak, Baran C. Saġlam, and Sevinç A. Türker. "Influence of QMix Irrigant on the Accuracy of Four Different Electronic Apex Locators." International Journal of Experimental Dental Science 5, no. 1 (2016): 23–27. http://dx.doi.org/10.5005/jp-journals-10029-1118.

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ABSTRACT The aim of this study was to compare the accuracy of four different electronic apex locators in the presence of various irrigation solutions or dry canal condition. Nineteen mandibular incisor teeth were selected. The real working lengths (RWL) of teeth were measured with #15 K-file. The electronic working lengths (EWLs) were measured with Root ZX mini, Raypex 6, iPex II, and Propex II under the condition of dry canal and in the presence of sodium hypochlorite and QMix. The difference between EWL and RWL was calculated. Root ZX mini was more accurate than Propex II under dry condition. No difference was found between the electronic apex locators in the presence of sodium hypochlorite (NaOCl). In the presence of QMix, Propex II and Root ZX mini demonstrated more accurate measurements than iPex II. Root ZX mini was found more accurate under dry condition than in the presence of QMix. Raypex 6 demonstrated more accuracy in the presence of QMix when compared with NaOCl. iPex II showed similar measurements with all tested solutions. Propex II was more accurate in the presence of QMix. All devices can be considered reliable when used with QMix irrigation solution and with any irrigant. How to cite this article Koçak MM, Koçak S, Sa?lam BC, Türker SA. Influence of QMix Irrigant on the Accuracy of Four Different Electronic Apex Locators. Int J Experiment Dent Sci 2016;5(1):23-27.

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Azis, Moh Ivan. "A boundary integral investigation for unsteady modified Helmholtz problems of some other classes of anisotropic functionally graded materials." International Journal of Computational Materials Science and Engineering 10, no. 01 (March 2021): 2150005. http://dx.doi.org/10.1142/s2047684121500056.

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Numerical solutions for a class of unsteady modified Helmholtz problems of anisotropic functionally graded materials are sought. The governing equation which is a variable coefficients equation is transformed to a constant coefficients equation. The time variable is transformed using the Laplace transform. The resulted partial differential equation of constant coefficients and time free variable is then converted to a boundary integral equation, from which boundary element solutions can be obtained. Some examples are considered to verify the accuracy, convergence and consistency of the numerical solutions. The results show that the numerical solutions are accurate, convergent and consistent.

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RASTIGEJEV, YEVGENII A., and SAMUEL PAOLUCCI. "WAVELET ADAPTIVE MULTIRESOLUTION REPRESENTATION: APPLICATIONS TO VISCOUS MULTISCALE FLOW SIMULATIONS." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 02 (June 2006): 333–43. http://dx.doi.org/10.1142/s0219691306001282.

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We present a new wavelet-based adaptive multiresolution representation (WAMR) algorithm for the numerical solution of multiscale evolution problems. Key features of the algorithm are fast procedures for grid rearrangement, computation of derivatives, as well as the ability to minimize the degrees-of-freedom for a prescribed solution accuracy. To demonstrate the efficiency and accuracy of the algorithm, we use it to solve the two-dimensional benchmark problem of incompressible fluid-flow in a lid-driven cavity at large Reynolds numbers. The numerical experiments demonstrate the great ability of the algorithm to adapt to different scales at different locations and at different times so as to produce accurate solutions at low computational cost. Specifically, we show that solutions of comparable accuracy as the benchmarks are obtained with more than an order of magnitude reduction in degrees-of-freedom.

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Akarsu, V., D. U. Sanli, and E. Arslan. "Accuracy of velocities from repeated GPS measurements." Natural Hazards and Earth System Sciences 15, no. 4 (April 21, 2015): 875–84. http://dx.doi.org/10.5194/nhess-15-875-2015.

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Abstract. Today repeated GPS measurements are still in use, because we cannot always employ GPS permanent stations due to a variety of limitations. One area of study that uses velocities/deformation rates from repeated GPS measurements is the monitoring of crustal motion. This paper discusses the quality of the velocities derived using repeated GPS measurements for the aim of monitoring crustal motion. From a global network of International GNSS Service (IGS) stations, we processed GPS measurements repeated monthly and annually spanning nearly 15 years and estimated GPS velocities for GPS baseline components latitude, longitude and ellipsoidal height. We used web-based GIPSY for the processing. Assuming true deformation rates can only be determined from the solutions of 24 h observation sessions, we evaluated the accuracy of the deformation rates from 8 and 12 h sessions. We used statistical hypothesis testing to assess the velocities derived from short observation sessions. In addition, as an alternative control method we checked the accuracy of GPS solutions from short observation sessions against those of 24 h sessions referring to statistical criteria that measure the accuracy of regression models. Results indicate that the velocities of the vertical component are completely affected when repeated GPS measurements are used. The results also reveal that only about 30% of the 8 h solutions and about 40% of 12 h solutions for the horizontal coordinates are acceptable for velocity estimation. The situation is much worse for the vertical component in which none of the solutions from campaign measurements are acceptable for obtaining reliable deformation rates.

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Jin, Qilin, and Weian Yao. "An accurate zigzag theory for bending and buckling analysis of thick laminated sandwich plates with soft core." Journal of Composite Materials 54, no. 18 (January 8, 2020): 2473–88. http://dx.doi.org/10.1177/0021998319899138.

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An accurate and computationally attractive zigzag theory is developed for bending and buckling analysis of thick laminated soft core sandwich plates. The kinematic assumptions of the proposed zigzag theory are obtained by superimposing a nonlinear zigzag function on the first-order shear deformation theory. In order to obtain the accurate transverse shear stresses, a preprocessing approach based on the three-dimensional equilibrium equations and the Reissner mixed variational theorem is used. It is significant that the second-order derivatives of in-plane displacement variables have been removed from the transverse shear stresses, such that the finite element implementation is greatly simplified. Thus, based on the proposed zigzag model, a computationally efficient four-node C0 quadrilateral plate element with linear interpolation function is proposed for bending and buckling analysis of soft core sandwich plates. The advantage of the present formulation is that no post-processing approach is needed to calculate the transverse shear stresses while maintaining the computational accuracy of a linear plate element. Moreover, the accurate transverse shear stresses can be involved in the strain energy which can actively improve the accuracy of critical loads. Performance of the proposed model is assessed by comparing with several benchmark solutions. Agreement between the present results and the reference solutions is very good, and the proposed model only includes the seven displacement variables which can demonstrate the accuracy and effectiveness of the proposed model.

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KHOKHLOV, A. M., and I. D. NOVIKOV. "SCALAR HYPERBOLIC EQUATION WITH GR-TYPE NONLINEARITY." International Journal of Modern Physics D 12, no. 10 (December 2003): 1889–903. http://dx.doi.org/10.1142/s0218271803004390.

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We study a scalar hyperbolic partial differential equation, [Formula: see text], with nonlinear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate balance between linear and nonlinear terms. We formulate two classes of second-order accurate central-difference schemes, CFLN and MOL, for numerical integration of this equation. Solutions produced by the schemes converge to exact solutions at any fixed time t when numerical resolution is increased. However, in certain cases integration becomes asymptotically unstable when t is increased and resolution is kept fixed. This behavior is caused by subtle changes in the balance between linear and nonlinear terms when the equation is discretized. Changes in the balance occur without violating second-order accuracy of discretization. We thus demonstrate that a second-order accuracy, althoug necessary for convergence at finite t, does not guarantee a correct asymptotic behavior and long-term numerical stability. Accuracy and stability of integration are greatly improved by an exponential transformation of the unknown variable.

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Taheri, Fatemeh, and Mohammad R. Hematiyan. "Torsional analysis of hollow members with sandwich wall." Journal of Sandwich Structures & Materials 19, no. 3 (January 11, 2017): 317–47. http://dx.doi.org/10.1177/1099636216688721.

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This paper proposes an analytical formulation for torsional analysis of thin-walled and moderately thick-walled hollow members with sandwich wall. The sandwich rod can have a complicated cross-section including straight and curved edges. The material and thickness of the two faces of the sandwich are assumed the same. Prandtl’s stress function is used to formulate the problem for faces and core, while the continuity and compatibility conditions at the face–core interfaces are also used to complete the formulation. By the presented method, it is possible to find the torsional stiffness and the shearing stress in the cross-section. By presenting several numerical examples, the accuracy of the presented method is demonstrated. The accuracy of the solutions resulting from the proposed method is demonstrated by comparing the results with accurate solutions obtained from the finite element method with a fine mesh. The effects of different geometrical and material parameters on the accuracy of the solutions are studied too. The presented formulation is quite practical and is employable for analyzing the torsion of thin- and moderately tick-walled sandwich members.

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Sideridis, George. "Direct Classroom Observation: Potential Problems and Solutions." Research in Education 59, no. 1 (May 1998): 19–28. http://dx.doi.org/10.1177/003452379805900103.

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Direct classroom observation: potential problems and solutions George Sideridis Direct observation has been the most widely used behavioural assessment method in education. The aim of this article is to define observer bias, drift and reactivity, using examples from the behaviour analytical literature, and suggest ways of controlling them. It concludes that the following recommendations can assist the reliable and accurate recording of student behaviour: (1) train observers intensively until they achieve high levels of reliability and accuracy, (2) use simple observational systems with as few behavioural categories as possible and simple operational definitions, (3) keep observers blind and experimenters double-blind to experimental conditions, subject characteristics, etc., (4) plan periodic training sessions for the observers to re-study the operational definition of behaviours and discuss the problems of the observation situation, (5) inform observers that all their observations are monitored, (6) use ‘real time’ observations and not time-sampling procedures, (7) keep observers motivated and reinforce them for accurate observation, and (8) have observers become part of the classroom environment beforehand.

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Choi, Jae-Young, Dong Kyun Im, Jangho Park, and Seongim Choi. "Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method." International Journal of Aerospace Engineering 2018 (August 1, 2018): 1–14. http://dx.doi.org/10.1155/2018/2508153.

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A mapped Chebyshev pseudospectral method is extended to solve three-dimensional unsteady flow problems. As the classical Chebyshev spectral approach can lead to numerical instabilities due to ill conditioning of the spectral matrix, the Chebyshev points are evenly redistributed over the domain by an inverse sine mapping function. The mapped Chebyshev pseudospectral method can be used as an alternative time-spectral approach that uses a Chebyshev collocation operator to approximate the time derivative terms in the unsteady flow governing equations, and the method can make general applications to both nonperiodic and periodic problems. In this study, the mapped Chebyshev pseudospectral method is employed to solve three-dimensional periodic problem to verify the spectral accuracy and computational efficiency with those of the Fourier pseudospectral method and the time-accurate method. The results show a good agreement with both of the Fourier pseudospectral method and the time-accurate method. The flow solutions also demonstrate a good agreement with the experimental data. Similar to the Fourier pseudospectral method, the mapped Chebyshev pseudospectral method approximates the unsteady flow solutions with a precise accuracy at a considerably effective computational cost compared to the conventional time-accurate method.

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Chen, Yanfei, Juan Zhang, and Hong Zhang. "Free vibration analysis of rotating tapered Timoshenko beams via variational iteration method." Journal of Vibration and Control 23, no. 2 (August 9, 2016): 220–34. http://dx.doi.org/10.1177/1077546315576431.

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Accurate determination of natural frequencies and mode shapes of the rotating tapered Timoshenko beam is important in engineering practice. This paper re-examines the free vibration of rotating tapered Timoshenko beams using the technique of variational iteration, which is relatively new and is capable of providing accurate solutions for eigenvalue problems in a quite easy way. Natural frequencies and mode shapes for rotating tapered Timoshenko beams with linearly varying height as well as linearly varying height and width are investigated via two numerical examples, and solutions are compared with results published in literature where available. Since the method constitutes a numerical procedure, the convergence of solutions which is important for practical implementation is evaluated as well, where efficiency and accuracy of variational iteration method in solving high order eigenvalue problems are demonstrated.

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Soltanalizadeh, Babak, Hadi Roohani Ghehsareh, Ahmet Yıldırım, and Saeid Abbasbandy. "On the Analytic Solution for a Steady Magnetohydrodynamic Equation." Zeitschrift für Naturforschung A 68, no. 6-7 (July 1, 2013): 412–20. http://dx.doi.org/10.5560/zna.2013-0014.

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The purpose of this study is to apply the Laplace-Adomian Decomposition Method (LADM) for obtaining the analytical and numerical solutions of a nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies. By using this method, the similarity solutions of the problem are obtained for some typical values of the model parameters. For getting computational solutions, we combined the obtained series solutions by LADM with the Padé approximation. The method is easy to apply and gives high accurate results. The presented results through tables and figures show the efficiency and accuracy of the proposed technique.

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DAVODI, A. G., D. D. GANJI, R. AZAMI, and H. BABAZADEH. "APPLICATION OF IMPROVED AMPLITUDE-FREQUENCY FORMULATION TO NONLINEAR DIFFERENTIAL EQUATION OF MOTION EQUATIONS." Modern Physics Letters B 23, no. 28 (November 10, 2009): 3427–36. http://dx.doi.org/10.1142/s0217984909021466.

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This paper presents an approach for solving accurate approximate analytical solutions for strong nonlinear oscillators called improved amplitude-frequency formulation. For illustrating the accuracy of the method, we also solved equations with He's energy balance method and compared results. New algorithms offer promising approaches, which are useful for nonlinear oscillations. We find that these attained solutions not only benefit from a high degree of accuracy, but are also uniformly valid in the whole solution domain which is so simple to do and effective. The studied equations are the general motion equation and the non-dimensional nonlinear differential equation of motion for the relativistic oscillator, which their solution can be useful for researchers to extend this ability into their other works.

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Motsa, Sandile S., and Precious Sibanda. "On Extending the Quasilinearization Method to Higher Order Convergent Hybrid Schemes Using the Spectral Homotopy Analysis Method." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/879195.

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We propose a sequence of highly accurate higher order convergent iterative schemes by embedding the quasilinearization algorithm within a spectral collocation method. The iterative schemes are simple to use and significantly reduce the time and number of iterations required to find solutions of highly nonlinear boundary value problems to any arbitrary level of accuracy. The accuracy and convergence properties of the proposed algorithms are tested numerically by solving three Falkner-Skan type boundary layer flow problems and comparing the results to the most accurate results currently available in the literature. We show, for instance, that precision of up to 29 significant figures can be attained with no more than 5 iterations of each algorithm.

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Isakari, Shirley M., and Richard C. J. Somerville. "Accurate numerical solutions for Daisyworld." Tellus B: Chemical and Physical Meteorology 41, no. 4 (July 1989): 478–82. http://dx.doi.org/10.3402/tellusb.v41i4.15103.

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ISAKARI, SHIRLEY M., and RICHARD C. J. SOMERVILLE. "Accurate numerical solutions for Daisyworld." Tellus B 41B, no. 4 (September 1989): 478–82. http://dx.doi.org/10.1111/j.1600-0889.1989.tb00324.x.

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Šedivá, A., Z. Panovská, and J. Pokorný. "Sensory profiles of sweeteners in aqueous solutions." Czech Journal of Food Sciences 24, No. 6 (November 12, 2011): 283–87. http://dx.doi.org/10.17221/3326-cjfs.

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Sensory profiles of saccharin, acesulfame K, aspartame, and neotame were compared with that of sucrose in three different types of water (tap water, commerical Crystalis water, and distilled water) under the conditions of the respective ISO standards. The intensities of off-flavours, especially bitter and metallic tastes, were higher in the solutions of synthetic sweeteners than in that of sucrose. The aspartame solution was the sample closest to the sucrose solution, and the intensity of off-flavours was significantly higher in acesulfame solution. Ratings of the bitter taste were related to those of the metallic taste, the relation being semilogarithmic. The performancies of different assessors were nearly the same in all ratings, and the absolute values of the ratings of sweetness and different off-flavours had the same repeatabilities. The relative accuracy was, naturally, much higher in off-flavours than in the case of sweetness.  

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Journal articles on the topic 'Solution's accuracy'

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