Journal articles: 'Analytické a numerické'

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Ryabov, Yu A. "Numeric-analytical construction of Mathieu functions." Mathematica Bohemica 124, no. 1 (1999): 15–28. http://dx.doi.org/10.21136/mb.1999.125982.

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Rowlands, R. E. "OS03W0436 Commingling thermoelasticity with other experimental, analytical and numerical tools." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2003.2 (2003): _OS03W0436. http://dx.doi.org/10.1299/jsmeatem.2003.2._os03w0436.

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Ambarita, Himsar. "Kajian Numerik Penguapan Pada Evaporator Desalinasi Air Laut Sistem Vakum Alami." Talenta Conference Series: Energy and Engineering (EE) 1, no. 1 (October 16, 2018): 095–103. http://dx.doi.org/10.32734/ee.v1i1.117.

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Fokus penelitian ini adalah alat desalinasi air laut energi surya dengan sistem vakum alami. Salah satu bagian terpenting yang menentukan performansi alat ini adalah proses penguapan pada kondisi vakum di dalam evaporator. Para peneliti umumnya menggunakan cara analitik dengan persamaan-persamaan empirik untuk menentukan laju penguapan pada evaporator.Padapenelitian ini diusulkan menggunakan metode numerik dengan menggunakan perangkat lunak CFD untuk menjelaskan proses penguapan pada evaporator. Hasil numerik dan analitik akan dibandingkan dengan hasil eksperimen. Peralatan eksperimen sederhana telah dirancang bangun untuk mendapatkan hasil eksperimen dan melakukan validasi. Hasil simulasi menunjukkan metode numerik dengan menggunakan perangkat lunak CFD dapat menggambarkan proses penguapan pada evaporator dengan baik. Perbandingan hasil analitik dan numerik menunjukkan laju penguapan di evaporator dengan metode numerik lebih dekat dengan hasil eksperimen. Metode numerik sebaiknya digunakan untuk melakukan inovasi agar dihasilkan peningkatan performansi desalinasi surya sistem vakum alami. The focus of this research is solar energy seawater desalination with a natural vacuum system. One of the most important parts that determine the performance of this tool is the evaporation process under vacuum inside the evaporator. Researchers generally use analytical methods with empirical equations to determine the evaporation rate of the evaporator. This research proposed by using a numerical method with CFD software to explain the evaporation process on evaporator. Numerical and analytical results will be compared with the experimental results. A simple experimental tool has been designed to get experimental results and validate. The simulation results show that the numerical method using CFD software can properly describe the evaporation process in the evaporator. Comparison of analytic and numerical results shows the evaporation rate in the evaporator with numerical methods closer to the experimental results. Numerical methods must be used to innovate so that the performance of solar desalination results increases by using a natural vacuum system.

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Jabbari, A., H. Kheiri, A. Jodayree Akbarfam, and A. Bekir. "Dynamical analysis of the avian–human influenza epidemic model using multistage analytical method." International Journal of Biomathematics 09, no. 06 (August 2, 2016): 1650090. http://dx.doi.org/10.1142/s179352451650090x.

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In this paper, analytical result of avian–human influenza epidemic model has been investigated by applying homotopy analysis method (HAM) and by expanding it to hybrid numeric-analytic method which is known as multistage HAM (MSHAM). HAM is an algorithm which gives us the approximate solution of the problem in an arrangement of time interims and by modifying it to multistage one. Some advantages such as flexibility of picking the auxiliary linear operator and the auxiliary parameter are emerged, that leads us to achieve some excellent results in this work. Furthermore, in this analytical work, obtained results are compared and reported with numerical ones which were obtained previously from methods such as the Runge–Kutta (RK4) method.

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Коrniyenko, Yu V., and M. G. Suryaninov. "Development of CAD implementing the algorithm of boundary elements’ numerical analytical method." Odes’kyi Politechnichnyi Universytet. Pratsi, no. 1 (March 31, 2015): 128–33. http://dx.doi.org/10.15276/opu.1.45.2015.21.

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NICOLAU, J. B., and E. VAN GROESEN. "HYBRID ANALYTIC-NUMERIC METHOD FOR LIGHT THROUGH A BOUNDED PLANAR DIELECTRIC STRUCTURE." Journal of Nonlinear Optical Physics & Materials 14, no. 02 (June 2005): 161–76. http://dx.doi.org/10.1142/s021886350500261x.

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We present a hybrid analytic-numeric method to calculate the transmission and reflection of light that is fluxed into a bounded complicated optical structure surrounded by air. The solution is obtained by numerical calculations inside a square containing the structure and by analytical calculations outside the square. For solving the 2D Helmholtz equation we formulate transparent-influx boundary conditions (TIBCs) on the boundaries of the square; these are incorporated into a variational formulation of the Helmholtz equation to obtain a FEM-implementation for the interior calculations.

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Alomari, A. K., M. S. M. Noorani, and R. Nazar. "On a New Reliable Algorithm." International Journal of Differential Equations 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/710250.

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An analytical expression for the solution of the prey-predator problem by an adaptation of the homotopy analysis method (HAM) is presented. The HAM is treated as an algorithm for approximating the solution of the problem in a sequence of time intervals; that is, HAM is converted into a hybrid numeric-analytic method called the multistage HAM (MSHAM). Comparisons between the MSHAM solutions and the fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear systems of ordinary differential equations.

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Lazareva, D. V., and M. G. Suryaninov. "Mathematical model of complex technical asymmetric system based on numerical-analytical boundary elements method." Odes’kyi Politechnichnyi Universytet. Pratsi, no. 2 (June 15, 2015): 133–37. http://dx.doi.org/10.15276/opu.2.46.2015.24.

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Pousti, Shahrouz, and Ali Jalali Marnani. "Numerical and Analytical Evaluation of Crude Oil Contamination Effect on Strip Foundation’s Bearing Capacity." International Journal of Scientific Research 3, no. 4 (June 1, 2012): 143–45. http://dx.doi.org/10.15373/22778179/apr2014/49.

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Papadaki, Maria-Evangelia, Nicolas Spyratos, and Yannis Tzitzikas. "Towards Interactive Analytics over RDF Graphs." Algorithms 14, no. 2 (January 25, 2021): 34. http://dx.doi.org/10.3390/a14020034.

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The continuous accumulation of multi-dimensional data and the development of Semantic Web and Linked Data published in the Resource Description Framework (RDF) bring new requirements for data analytics tools. Such tools should take into account the special features of RDF graphs, exploit the semantics of RDF and support flexible aggregate queries. In this paper, we present an approach for applying analytics to RDF data based on a high-level functional query language, called HIFUN. According to that language, each analytical query is considered to be a well-formed expression of a functional algebra and its definition is independent of the nature and structure of the data. In this paper, we investigate how HIFUN can be used for easing the formulation of analytic queries over RDF data. We detail the applicability of HIFUN over RDF, as well as the transformations of data that may be required, we introduce the translation rules of HIFUN queries to SPARQL and we describe a first implementation of the proposed model.

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Ene, Remus-Daniel, Camelia Pop, and Camelia Petrişor. "Systematic Review of Geometrical Approaches and Analytical Integration for Chen’s System." Mathematics 8, no. 9 (September 8, 2020): 1530. http://dx.doi.org/10.3390/math8091530.

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The main goal of this paper is to present an analytical integration in connection with the geometrical frame given by the Hamilton–Poisson formulation of a specific case of Chen’s system. In this special case we construct an analytic approximate solution using the Multistage Optimal Homotopy Asymptotic Method (MOHAM). Numerical simulations are also presented in order to make a comparison between the analytic approximate solution and the corresponding numerical solution.

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Ftorek, Branislav, Pavol Oršanský, and Helena Šamajová. "Parametric oscillations of the mechanical systems." MATEC Web of Conferences 157 (2018): 08002. http://dx.doi.org/10.1051/matecconf/201815708002.

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This paper deals with an approximative solution in the analytical form of some second order linear differential equation with time depend parameters. The analytic solution is compared with the numerical solution obtained by Runge-Kutta method and the conditions of the convergence of this analytical method are discussed.

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Ningsi, Gabariela Purnama, Fransiskus Nendi, and Lana Sugiarti. "An application of the finite difference method for solving the mass spring system equation." Jurnal Matematika, Statistika dan Komputasi 16, no. 3 (April 28, 2020): 404. http://dx.doi.org/10.20956/jmsk.v16i3.9574.

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The numerical method is one method that can be used to solve differential equations, both differential equations that are easy or difficult to solve analytically. The solution obtained from the calculation results is an approximate solution or a solution that approaches an analytic solution, not an analytic solution. That is, in solving differential equations numerically, there is always an error. In this paper, an analytical solution is described and described and the application of different methods in solving a damped mass spring system with a known limit value. The error between the analytic and numerical solutions obtained is very small.

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Jódar, Lucas, Enrique Navarro, and M. V. Ferrer. "A matrix constructive method for the analytic-numerical solution of coupled partial differential systems." Applications of Mathematics 40, no. 5 (1995): 391–400. http://dx.doi.org/10.21136/am.1995.134302.

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Moradi, Amir, and Reza Rafiee. "Analytical solution to convection-radiation of a continuously moving fin with temperature-dependent thermal conductivity." Thermal Science 17, no. 4 (2013): 1049–60. http://dx.doi.org/10.2298/tsci110425005m.

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In this article, the simultaneous convection-radiation heat transfer of a moving fin of variable thermal conductivity is studied. The differential transformation method (DTM) is applied for an analytic solution for heat transfer in fin with two different profiles. Fin profiles are rectangular and exponential. The accuracy of analytic solution is validated by comparing it with the numerical solution that is obtained by fourth-order Runge-Kutta method. The analytical and numerical results are shown for different values of the embedding parameters. DTM results show that series converge rapidly with high accuracy. The results indicate that the fin tip temperature increases when ambient temperature increases. Conversely, the fin tip temperature decreases with an increase in the Peclet number, convection-conduction and radiation-conduction parameters. It is shown that the fin tip temperature of the exponential profile is higher than the rectangular one. The results indicate that the numerical data and analytical method are in a good agreement with each other.

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Siakavellas, Nicolaos J. "The Importance of Analytic Solutions for Verification: Application to the Secondary Magnetic Flux of a Conductive Disk." International Journal of Electrical Engineering & Education 44, no. 4 (October 2007): 342–57. http://dx.doi.org/10.7227/ijeee.44.4.5.

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The method and value of analytical methods and the importance of analytic solutions for verification must be emphasised to both under- and post-graduate students. So, they must be able to: (i) derive by their own expressions for the quantities of interest, and (ii) test their numerical results by an independent method. Hence, they must be motivated to try to solve any problem analytically, before proceeding to a numerical solution. Towards this aim, a sample problem is proposed and an analytic expression is derived for the secondary magnetic flux induced in a conductive disk by a time-varying magnetic field. This expression, involving elliptic and improper integrals, is finally reduced into a single integral, depending on the current distribution on the disk. Next, an analytical solution for a simplified version of the problem is obtained, which may be used for verification of the numerical solution of the more complex and general problem.

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NUNES, R. P., and F. B. RIZZATO. "Analytical method for determining at equilibrium the envelope and emittance of initially mismatched beams." Journal of Plasma Physics 75, no. 6 (June 3, 2009): 829–39. http://dx.doi.org/10.1017/s0022377809990079.

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AbstractThis work presents a fully analytic way of determining relevant equilibrium quantities of a high-intensity charged particle beam submitted to magnetic focusing while inside a linear channel. Through the current approach, some intermediate steps of our original hybrid model which had to be solved numerically can now be eliminated, leading to the obtainment of a fully analytic expression. This expression relates the initial beam parameters with those at equilibrium, allowing beam macroscopic quantities such as envelope and emittance to be naturally and analytically determined. For validation, full self-consistent N-particle beam numerical simulations have been carried out and the results compared with the predictions supplied by the full analytical model. The agreement is shown to be good with the simulations and also with the original hybrid numerical-analytical version of the model.

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Parker, A. P., and X. Huang. "Autofrettage and Reautofrettage of a Spherical Pressure Vessel." Journal of Pressure Vessel Technology 129, no. 1 (March 10, 2006): 83–88. http://dx.doi.org/10.1115/1.2389020.

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There is a numerical procedure for modeling autofrettage of thick-walled cylinders that incorporates the Bauschinger effect as a function of prior plastic strain and Von Mises’ yield criterion. In this paper the numerical procedure is extended to solve the analogous problem of a spherical, thick walled steel vessel. An equivalent new analytical solution for the case of a spherical vessel is also formulated. The analytical and numerical solutions are shown to be in close agreement. It is demonstrated numerically that a reautofrettage procedure, previously proposed for cylindrical vessels, may be extremely beneficial for spherical vessels. Additional commentary is provided on the limitations of certain analytic solutions.

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DEAN, D. J., C. BOTTCHER, and M. R. STRAYER. "SPLINE TECHNIQUES FOR SOLVING RELATIVISTIC CONSERVATION EQUATIONS." International Journal of Modern Physics C 04, no. 04 (August 1993): 723–47. http://dx.doi.org/10.1142/s0129183193000616.

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We discuss a new numerical method for solving the relativistic hydrodynamic equations based upon the basis-spline collocation approach. Analytical and numerical results are compared for several problems, including one-dimensional expansions and collisions for which analytical solutions exist. Our methods, which may be easily and massively parallelized, are shown to give numerical results which agree to within a few percent of the analytic solutions. We discuss the relevance of the υ = z/t scaling solutions for the one-dimensional problem when applied to relativistic heavy-ion collisions. Finally, we discuss applications to three-dimensional problems, and present results for a typical three-dimensional expansion.

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LUPU, Mircea, Gheorghe RADU, and Cristian-George CONSTANTINESCU. "ANALYTIC-NUMERIC METHODS IN THE VALIDATION OF ANY FLOW REGIMES IN HYDRO-AERODYNAMICS." SCIENTIFIC RESEARCH AND EDUCATION IN THE AIR FORCE 19, no. 1 (July 31, 2017): 379–88. http://dx.doi.org/10.19062/2247-3173.2017.19.1.46.

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del Rio, Ezequiel, and Sergio Elaskar. "On the Theory of Intermittency in 1D Maps." International Journal of Bifurcation and Chaos 26, no. 14 (December 30, 2016): 1650228. http://dx.doi.org/10.1142/s021812741650228x.

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The classical theory of intermittency developed for return maps assumes uniform density of points reinjected from the chaotic to laminar region. Recently, we reported how the reinjection probability density (RPD) can be generalized. Estimation of the universal RPD is based on fitting a linear function to experimental or numerical data. Here we present an analytical approach to estimate the RPD. After this, we can get an analytic evaluation of the characteristic exponent traditionally used to characterize the intermittency type. The proposed theoretical method is general and very simple to use. It is compared with numerical computation, showing a good agreement between both. Our analytical results are compared with some celebrated classical numerical results on intermittency theory.

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Kwapisz, Marian. "On modification of Samoilenko's numerical-analytic method of solving boundary value problems for difference equations." Applications of Mathematics 38, no. 2 (1993): 133–44. http://dx.doi.org/10.21136/am.1993.104540.

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Oršanský, Pavol, and Branislav Ftorek. "Compare of analytic and numerical solution of parametric oscillator with perturbation and its analytical solution." MATEC Web of Conferences 254 (2019): 08003. http://dx.doi.org/10.1051/matecconf/201925408003.

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In this paper we deal with an approximative analytical solution of a second order differential equation with a fast time periodic modulation. We use for this type of the equation a homotopy perturbation method. The validity of this approximative solution is verified by numerical experiments, where we achieve considerable consistency of doth soliutions.

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LIU, SAN-QIU, and XIAO-CHANG CHEN. "Dispersion relation of transverse oscillation in relativistic plasmas with non-extensive distribution." Journal of Plasma Physics 77, no. 5 (February 15, 2011): 653–62. http://dx.doi.org/10.1017/s0022377811000043.

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AbstractThe generalized dispersion equation for superluminal transverse oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma with non-extensive q-distribution is derived. The analytical dispersion relation is obtained in an ultra-relativistic regime, which is related to q-parameter and temperature. In the limit q → 1, the result based on the relativistic Maxwellian distribution is recovered. Using the numerical method, we obtain the full dispersion curve that cannot be given by an analytic method. It is shown that the numerical solution is in good agreement with the analytical result in the long-wavelength and short-wavelength region for ultra-relativistic plasmas.

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Xu, Guo Fu, Zheng Dong Deng, Chong Ji, and Jing Jing Jia. "Research on Analytic Calculation Method of the Dynamic Response of Buried Pipelines under Indirect Ground Shock." Applied Mechanics and Materials 477-478 (December 2013): 77–80. http://dx.doi.org/10.4028/www.scientific.net/amm.477-478.77.

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Buried pipelines are important lifeline engineering. During war conventional weapons blasting in the air would induce indirect ground shock, and the shock to the buried pipeline can lead to the paralyzed of urban economic and social function. And the numerical simulation of the dynamic damage of buried pipeline is complicated and time consuming, so this article using the equivalent static load method proposes analytic solution method of stress calculation of buried pipeline under ground shock. Through comparing the results calculated by analytic solution method and numerical solution, it shows that the analytical solution is feasible in engineering application.

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Rakisheva, D. S., Igor N. Modin, and B. G. Mukanova. "Mapes of secondary sources in the problem of ERT probing 2D medium: numerical method and analytical solutions." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 98, no. 2 (June 30, 2020): 204–13. http://dx.doi.org/10.31489/2020m2/204-213.

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González Parra, Gilberto, Abraham J. Arenas, and Miladys Cogollo. "Analytical-Numerical Solution of a Parabolic Diffusion Equation Under Uncertainty Conditions Using DTM with Monte Carlo Simulations." Ingeniería y Ciencia 11, no. 22 (July 31, 2015): 49–72. http://dx.doi.org/10.17230/ingciencia.11.22.3.

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A numerical method to solve a general random linear parabolic equationwhere the diffusion coefficient, source term, boundary and initial condi-tions include uncertainty, is developed. Diffusion equations arise in manyfields of science and engineering, and, in many cases, there are uncertaintiesdue to data that cannot be known, or due to errors in measurements andintrinsic variability. In order to model these uncertainties the correspon-ding parameters, diffusion coefficient, source term, boundary and initialconditions, are assumed to be random variables with certainprobabilitydistributions functions. The proposed method includes finite differenceschemes on the space variable and the differential transformation methodfor the time. In addition, the Monte Carlo method is used to deal withthe random variables. The accuracy of the hybrid method is investigatednumerically using the closed form solution of the deterministic associated equation. Based on the numerical results, confidence intervals and ex-pected mean values for the solution are obtained. Furthermore, with theproposed hybrid method numerical-analytical solutions are obtained.

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Haning, Ady E. P., and Ali Warsito. "Comparation of Magnetic Flux Cases Solution in Around Electrified Wire between Analytical and Computational Methods." Jurnal ILMU DASAR 19, no. 1 (February 23, 2018): 23. http://dx.doi.org/10.19184/jid.v19i1.6338.

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Have analyzed comparative analytical and numerical computation solutions in the case of magnetic flux to the circular loop of radius R as far apart as H around the current I in the wire. The aim is to know how the methods used have an accurate solutions calculated based on relative error value. The analytical method use taking concept of polar coordinates and the computational method using the function of analytic equations modified based on Simpson and Monte Carlo method. Both methods are aprroaches in numerical integration.After test with variation of combination of R=0.1 and 0.2 and H=0.1 and 0.2, the Simpson and Monte Carlo indicate the integration value corresponding to the exact or analytical solution value, the relative error value of the Simpson method range from 0,004% - 0,017% and the relatif error value for Monte Carlo method range from 0.056% - 3.4296%. Keywords: magnetic flux, analytical, simpson, monte carlo, relative error

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Jeremić, Olivera, Momčilo Milinović, Miloš Marković, and Boško Rašuo. "Analytical and numerical method of velocity fields for the explosively formed projectiles." FME Transactions 45, no. 1 (2017): 38–44. http://dx.doi.org/10.5937/fmet1701038j.

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KASCHENKO, D., S. KASCHENKO, and W. SCHWARZ. "DYNAMICS OF FIRST ORDER EQUATIONS WITH NONLINEAR DELAYED FEEDBACK." International Journal of Bifurcation and Chaos 22, no. 08 (August 2012): 1250184. http://dx.doi.org/10.1142/s0218127412501842.

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In this paper, we have studied an important class of first order differential equations with nonlinear delayed feedback. The nonlocal dynamics of such equations was investigated by analytical and numeric–analytical methods. An approach based on asymptotic analysis made it possible to study attractors consisting of impulse type solutions. We obtained some numerical characteristics of irregular oscillations and studied their dependence on the delay.

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Zhang, Dongmei, and Fangqi Chen. "Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance." Journal of Applied Mathematics 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/414903.

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Stability and bifurcation behaviors for a model of simply supported functionally graded materials rectangular plate subjected to the transversal and in-plane excitations are studied by means of combination of analytical and numerical methods. The resonant case considered here is 1 : 1 internal resonances and primary parametric resonance. Two types of degenerated equilibrium points are studied in detail, which are characterized by a double zero and two negative eigenvalues, and a double zero and a pair of pure imaginary eigenvalues. For each case, the stability regions of the initial equilibrium solution and the critical bifurcation curves are obtained in terms of the system parameters which may lead to Hopf bifurcation and 2D torus. With both analytical and numerical methods, bifurcation behaviors on damping parameters and detuning parameters are studied, respectively. A time integration scheme is used to find the numerical solutions for these bifurcation cases, and numerical results agree with the analytic predictions.

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Li, Qiang, Yu Gu, and Nanfei Wang. "Free Vibration Analysis of a New Polymer Quartz Piezoelectric Crystal Sensor Applied to Identify Chinese Liquors." International Journal of Applied Mechanics 09, no. 01 (January 2017): 1750015. http://dx.doi.org/10.1142/s1758825117500156.

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This paper deals with the analytical and numerical analysis of free vibration in a new polymer piezoelectric crystal sensor. A quartz piezoelectric crystal here serves as the basal material and nonmetallic polymer thin films with perforative central holes as the surface coating according to the principle of quartz crystal microbalance (QCM), based on the Kirchhoff–Love plate model. A mechanical model of the new sensor was built, and its structure was a quartz piezoelectric sandwich composite circular plate with perforative central holes in the surface layers. The form of the electric potential field in the piezoelectric layer was here assumed to be such that the Maxwell static electricity equation is satisfied. The validation of the mechanical model and its analytic method is conducted by comparing the free vibration frequencies of the piezoelectric sandwich composite circular plate produced by the mechanical model’s analytical and numerical analyses performed using ANSYS software. Results show that the first 100 orders of free vibration frequency values of the mechanical model obtained by two methods, the analytical analysis and the numerical analysis, to be fit. The maximum absolute deviation rate ([Formula: see text] between the analytical solutions ([Formula: see text]) and the numerical solutions ([Formula: see text]) was found to be 6.89%. These results are important reference for the design of the new polymer quartz piezoelectric crystal sensors suitable for the identification of Chinese liquors.

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Amer, W. S. "On the Harmonic Oscillations for the Motion of a Dynamical System." JOURNAL OF ADVANCES IN PHYSICS 13, no. 2 (March 16, 2017): 4657–70. http://dx.doi.org/10.24297/jap.v13i2.5754.

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This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

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Khatami, I., M. H. Pashai, and N. Tolou. "Comparative Vibration Analysis of a Parametrically Nonlinear Excited Oscillator Using HPM and Numerical Method." Mathematical Problems in Engineering 2008 (2008): 1–11. http://dx.doi.org/10.1155/2008/956170.

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The objective of this paper is to present an analytical investigation to analyze the vibration of parametrically excited oscillator with strong cubic negative nonlinearity based on Mathieu-Duffing equation. The analytic investigation was conducted by using He's homotopy-perturbation method (HPM). In order to obtain the analytical solution of Mathieu-Duffing equation, homotopy-perturbation method has been utilized. The Runge-Kutta's (RK) algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution. Afterward, the effects of variation of the parameters on the accuracy of the homotopy-perturbation method were studied.

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Motsa, S. S., and S. Shateyi. "New Analytic Solution to the Lane-Emden Equation of Index 2." Mathematical Problems in Engineering 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/614796.

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We present two new analytic methods that are used for solving initial value problems that model polytropic and stellar structures in astrophysics and mathematical physics. The applicability, effectiveness, and reliability of the methods are assessed on the Lane-Emden equation which is described by a second-order nonlinear differential equation. The results obtained in this work are also compared with numerical results of Horedt (1986) which are widely used as a benchmark for testing new methods of solution. Good agreement is observed between the present results and the numerical results. Comparison is also made between the proposed new methods and existing analytical methods and it is found that the new methods are more efficient and have several advantages over some of the existing analytical methods.

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Rao, K. Kondala, and K. Lakshmi Narayan. "Stability Analysis of a Three Species Syn-Eco Dynamical System with a Limited Alternative Food for all the Three Species." Bulletin of Society for Mathematical Services and Standards 1 (March 2012): 14–20. http://dx.doi.org/10.18052/www.scipress.com/bsmass.1.14.

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The present paper is devoted to an analytic investigation of a three species syn-eco system comprising two mutually helping species, both amensol on a third species. All possible equilibrium points are identified and their stability criteria is discussed by using Routh-Hurwitz criteria. Further, the analytical results are supported by numerical simulation using Mat Lab.

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Ma, Lian Hua, Bernard F. Rolfe, Qing Sheng Yang, and Chun Hui Yang. "A New Solution Method for Homogenization of Effective Properties of Electromagnetic Honeycombs." Key Engineering Materials 443 (June 2010): 551–56. http://dx.doi.org/10.4028/www.scientific.net/kem.443.551.

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In this paper, an analytical model and its new numerical solution using the homogenization method are developed to determine the effective electromagnetic characteristics of honeycombs. Based on the proposed solution method, the electromagnetic properties are obtained by employing the multi-scale homogenization theory and periodical electric (magnetic) potential boundary conditions. Further, the effect of geometry of honeycomb’s unit cell on effective electromagnetic properties is investigated with the use of the proposed method. The numerical results are compared with analytic results using the Smith-Scarpa’s semi-empirical formula.

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Das, R. N., and G. Pradhan. "Numerical quadrature of analytic functions." International Journal of Mathematical Education in Science and Technology 29, no. 4 (July 1998): 569–74. http://dx.doi.org/10.1080/0020739980290408.

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39

Giorgini, L. T., W. Moon, and J. S. Wettlaufer. "Analytical Survival Analysis of the Ornstein–Uhlenbeck Process." Journal of Statistical Physics 181, no. 6 (November 5, 2020): 2404–14. http://dx.doi.org/10.1007/s10955-020-02669-y.

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AbstractWe use asymptotic methods from the theory of differential equations to obtain an analytical expression for the survival probability of an Ornstein–Uhlenbeck process with a potential defined over a broad domain. We form a uniformly continuous analytical solution covering the entire domain by asymptotically matching approximate solutions in an interior region, centered around the origin, to those in boundary layers, near the lateral boundaries of the domain. The analytic solution agrees extremely well with the numerical solution and takes into account the non-negligible leakage of probability that occurs at short times when the stochastic process begins close to one of the boundaries. Given the range of applications of Ornstein–Uhlenbeck processes, the analytic solution is of broad relevance across many fields of natural and engineering science.

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40

Ranatowski, Eugeniusz. "Problems of welding in shipbuilding - an analytic-numerical assessment of the thermal cycle in HAZ with three dimensional heat source models in agreement with modelling rules." Polish Maritime Research 17, no. 3 (January 1, 2010): 45–52. http://dx.doi.org/10.2478/v10012-010-0027-y.

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Problems of welding in shipbuilding - an analytic-numerical assessment of the thermal cycle in HAZ with three dimensional heat source models in agreement with modelling rules This part is continuation of PART II. Analytic solutions for the temperature distribution in HAZ - presented in the previous part of this article are transformed for computer calculation with used Mathcad programme. There are established algorithms in moving and stationary systems for thermal cycle calculating. Finally, a few analytical examples with use of C-I-N and D-E models are demonstrated.

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Mustafa, M. T., A. F. M. Arif, and Khalid Masood. "Approximate Analytic Solutions of Transient Nonlinear Heat Conduction with Temperature-Dependent Thermal Diffusivity." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/423421.

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A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars made of stainless steel AISI 304 and mild steel. The results from the approximate analytical solutions and the numerical solution are compared indicating good agreement.

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42

Ghiasi, Pedram, Gholamhassan Najafi, Barat Ghobadian, and Ali Jafari. "Analytical and Numerical Solution for H-type Darrieus Wind Turbine Performance at the Tip Speed Ratio of Below One." International Journal of Renewable Energy Development 10, no. 2 (December 30, 2020): 269–81. http://dx.doi.org/10.14710/ijred.2021.33169.

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H-type Darrieus vertical axis wind turbines (VAWT) have omnidirectional movement capability and can get more power compared to other VAWTs at high tip speed ratios (𝜆). However, its disadvantages are self-starting inability and low generated power at 𝜆 less than 1. The performance of H-type Darrieus wind turbine at 𝜆<1 was studied using double multiple stream tube (DMST) model and two-dimensional computational fluid dynamic (CFD) simulation. In CFD simulation, the Unsteady Reynolds Averaged Navier-Stokes (URANS) equations were used and the turbulence model was solved with SST k-ω model. The performance of fifteen various wind turbines was determined at fourteen wind velocities by two solution methods. The effect of chord length, solidity, Reynolds number and Height to Diameter (H/D) ratio were investigated on generated torque, power and the time required to reach 𝜆=0.1. Increasing in the moment of inertia due to the increasing in required time to reach 𝜆=0.1. In the low TSRs, the wind turbines can generate higher torque and power in high Re numbers and solidities. The required time was reduced by an increase in Re number and solidity. Finally, the best ratio of H/D of H-type Darrieus wind turbines was defined to improve the turbine performance.

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TIMKOV, V. F. "ANALYTICAL EVALUATION OF THE NUMERICAL VALUES OF THE HUBBLE CONSTANT AND MAIN SPATIAL-ENERGY CHARACTERISTICS OF THE OBSERVABLE UNIVERSE." Digital Technologies 26 (2019): 7–21. http://dx.doi.org/10.33243/2313-7010-26-7-21.

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Since the baryonic matter of the observable Universe consists mainly of protons and neutrons, then the numerical value of its mass can be represented and calculated on the basis of an additive-multiplicative golden algebraic fractal, based on golden algebraic fractals of the masse of proton, neutron, and muon. Based on an analytical estimate of the mass of the observable Universe, using the law “Planck’s Universal Proportions”, an analytical estimate of the Hubble constant and the main spatial-energy characteristics of the observed Universe is obtained. An analytical estimate of the Hubble constant is consistent with the experimental data of Planck’s mission, SDSS-III Baryon Oscillation Spectroscopic Survey, DES Collaboration. The objectivity of the experimental estimation of the Hubble constant from the H0LiCOW, Riess et al, Hubble Space Telescope collaborations does not raise any doubts. This means that the Hubble constant describes two similar, but different physical processes and has at least two values. The value of the Hubble constant from the collaborations Planck’s mission, SDSS-III Baryon Oscillation Spectroscopic Survey, DES Collaboration describes the process of rotation of the space of the observed Universe, and the value of the Hubble constant from the collaborations H0LiCOW, Riess et al, Hubble Space Telescope describes the process of rotation of substance in the space of the observed Universe. It is shown that after the Big Bang, the space of the observable Universe made one incomplete revolution of at 345 degrees, and the substance in it made one complete revolution of approximately 379 degrees. New estimates are given: of the gravitational constant, of the Planck energy, of the Planck acceleration, of the Planck force, of the gravity factor of the observable Universe, of the Planck temperature, of the angular velocity of rotation of the space of the observable Universe. Estimates of temperature and wavelength of thermal radiation of the observable Universe, as the Hubble sphere, are given.

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Ebner, H. "THE ANALYTICAL PLOTTER AND NUMERICAL PHOTOGRAMMETRY." Photogrammetric Record 10, no. 58 (August 26, 2006): 409–20. http://dx.doi.org/10.1111/j.1477-9730.1981.tb00140.x.

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Vanden, Kirk J., and Paul D. Orkwis. "Comparison of numerical and analytical Jacobians." AIAA Journal 34, no. 6 (June 1996): 1125–29. http://dx.doi.org/10.2514/3.13202.

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Golestani Dariani, A. A., and M. M. Ahmadi. "CPT Cone Factor: Numerical-Analytical Approach." International Journal of Geomechanics 19, no. 12 (December 2019): 04019132. http://dx.doi.org/10.1061/(asce)gm.1943-5622.0001521.

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Fathi, Nima, Seyed Sobhan Aleyasin, and Peter Vorobieff. "Numerical–analytical assessment on Manzanares prototype." Applied Thermal Engineering 102 (June 2016): 243–50. http://dx.doi.org/10.1016/j.applthermaleng.2016.03.133.

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Mehri, Sondos, Ahmed Chiheb Ammari, Jaleleddine Ben Hadj Slama, and Hatem Rmili. "Geometry Optimization Approaches of Inductively Coupled Printed Spiral Coils for Remote Powering of Implantable Biomedical Sensors." Journal of Sensors 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/4869571.

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Electronic biomedical implantable sensors need power to perform. Among the main reported approaches, inductive link is the most commonly used method for remote powering of such devices. Power efficiency is the most important characteristic to be considered when designing inductive links to transfer energy to implantable biomedical sensors. The maximum power efficiency is obtained for maximum coupling and quality factors of the coils and is generally limited as the coupling between the inductors is usually very small. This paper is dealing with geometry optimization of inductively coupled printed spiral coils for powering a given implantable sensor system. For this aim, Iterative Procedure (IP) and Genetic Algorithm (GA) analytic based optimization approaches are proposed. Both of these approaches implement simple mathematical models that approximate the coil parameters and the link efficiency values. Using numerical simulations based on Finite Element Method (FEM) and with experimental validation, the proposed analytic approaches are shown to have improved accurate performance results in comparison with the obtained performance of a reference design case. The analytical GA and IP optimization methods are also compared to a purely Finite Element Method based on numerical optimization approach (GA-FEM). Numerical and experimental validations confirmed the accuracy and the effectiveness of the analytical optimization approaches to design the optimal coil geometries for the best values of efficiency.

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Bisadi, H., and M. Khaleghi Meybodi. "Experimental, numerical, and theoretical analyses of simultaneous forming–welding of inhomogeneous plates." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 11 (September 27, 2011): 2552–64. http://dx.doi.org/10.1177/0954406211403667.

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Experimental tests for simultaneous explosive forming–welding for two inhomogeneous plates have been carried out. Sheets of copper, aluminium, and steel were used for simultaneous forming and welding. Also, analytical and numerical analyses were conducted. Given analytic model, is based on energy method, and considering support conditions, deformation, and critical amount of impacts. Two metal plates are converted to their equivalent homogeneous plate by a method similar to the analysis of combined beams. On the other hand, finite-element analysis has been done wherein the work plates have been modelled by Johnson–Cook material model. The maximum deformation of plates and the possibility of rupture have been predicted with respect to mechanical properties of the plates. Also, to measure the velocity of flyer plate, which is necessary to compute impact, an innovative method is presented. Then, the amounts of experimental deformation, stresses, and strains were compared with analytical and numerical results and rather good similarities have been observed.

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Lv, Guang Hong, and Xiao Bo Lv. "Performance Analyses of MCN with PH-Renewal Arrival Call and Services." Advanced Materials Research 1044-1045 (October 2014): 1229–34. http://dx.doi.org/10.4028/www.scientific.net/amr.1044-1045.1229.

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For the mobile cellular networks (MCN), a new analytical model which is the PH-renewal process to model is developed in this paper as a cost-effective performance tool to investigate the performance of the MCN. To the best of our knowledge, we have not found to analyze the performance of the MCN by the pure PH-renewal models. We apply the matrix-analytic approach and the PH-renewal process to explore the performance measure of the drop and block probabilities in the MCN. The numerical results show that the proposed analytical approach is more efficient than others.

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Journal articles on the topic 'Analytické a numerické'

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