Relevant bibliographies by topics / PDEs and ODEs numerical method

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'PDEs and ODEs numerical method'

Author: Grafiati
Published: 22 February 2023

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Journal articles on the topic "PDEs and ODEs numerical method"

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Wang, Xiaofeng. "Fixed-Point Iterative Method with Eighth-Order Constructed by Undetermined Parameter Technique for Solving Nonlinear Systems." Symmetry 13, no. 5 (2021): 863. http://dx.doi.org/10.3390/sym13050863.

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In this manuscript, by using undetermined parameter method, an efficient iterative method with eighth-order is designed to solve nonlinear systems. The new method requires one matrix inversion per iteration, which means that computational cost of our method is low. The theoretical efficiency of the proposed method is analyzed, which is superior to other methods. Numerical results show that the proposed method can reduce the computational time, remarkably. New method is applied to solve the numerical solution of nonlinear ordinary differential equations (ODEs) and partial differential equations
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Ahmad, Imtiaz, Muhammad Riaz, Muhammad Ayaz, Muhammad Arif, Saeed Islam, and Poom Kumam. "Numerical Simulation of Partial Differential Equations via Local Meshless Method." Symmetry 11, no. 2 (2019): 257. http://dx.doi.org/10.3390/sym11020257.

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In this paper, numerical simulation of one, two and three dimensional partial differential equations (PDEs) are obtained by local meshless method using radial basis functions (RBFs). Both local and global meshless collocation procedures are used for spatial discretization, which convert the given PDEs into a system of ODEs. Multiquadric, Gaussian and inverse quadratic RBFs are used for spatial discretization. The obtained system of ODEs has been solved by different time integrators. The salient feature of the local meshless method (LMM) is that it does not require mesh in the problem domain an
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Chen, Yong, and Jianjun Ma. "Numerical Contour Integral Methods for Free-Boundary Partial Differential Equations Arising in American Volatility Options Pricing." Discrete Dynamics in Nature and Society 2018 (November 4, 2018): 1–12. http://dx.doi.org/10.1155/2018/1838521.

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The aim of this paper is to study the numerical contour integral methods (NCIMs) for solving free-boundary partial differential equations (PDEs) from American volatility options pricing. Firstly, the governing free-boundary PDEs are modified as a unified form of PDEs on the fixed space region; then performing Laplace-Carson transform (LCT) leads to ordinary differential equations (ODEs) which involve the unknown inverse functions of free boundaries. Secondly, the inverse free-boundary functions are approximated and optimized by solving of the free-boundary values of the perpetual American vola
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Enright, W. H. "On the use of ‘arc length’ and ‘defect’ for mesh selection for differential equations." Computing Letters 1, no. 2 (2005): 47–52. http://dx.doi.org/10.1163/1574040054047586.

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In this note we will consider mesh selection techniques for ordinary differential equations (ODEs) and for partial differential equations (PDEs) based on arc length and defect. We assume we are trying to approximate y(x) for x ϵ [0; T] in the ODE case and u(x; y) for (x; y) ϵ Ω in the PDE case. The two specific areas of application that we have in mind are the numerical solution of boundary value problems (BVPs) in ODEs and the numerical solution of PDEs when a method of lines (MOL) approach is employed. The approach we develop is applicable to a wider class of PDEs including mixed-order probl
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Iqbal, Mazhar, M. T. Mustafa, and Azad A. Siddiqui. "A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/105414.

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Standard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures available to utilize these numerical solutions of reduced ODE to obtain the solution of original PDE. A practical and tractable approach is proposed to deal with such situations and is applied to obtain approximate similarity solutions to different cases of an initial-boundary value problem of unsteady gas
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Wang, Naige, Guohua Cao, Lu Yan, and Lei Wang. "Modeling and Control for a Multi-Rope Parallel Suspension Lifting System under Spatial Distributed Tensions and Multiple Constraints." Symmetry 10, no. 9 (2018): 412. http://dx.doi.org/10.3390/sym10090412.

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The modeling and control of the multi-rope parallel suspension lifting system (MPSLS) are investigated in the presence of different and spatial distributed tensions; unknown boundary disturbances; and multiple constraints, including time varying geometric constraint, input saturation, and output constraint. To describe the system dynamics more accurately, the MPSLS is modelled by a set of partial differential equations and ordinary differential equations (PDEs-ODEs) with multiple constraints, which is a nonhomogeneous and coupled PDEs-ODEs, and makes its control more difficult. Adaptive bounda
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Govardhan, Kamatam, Ganji Narender, and Gobburu Sreedhar Sarma. "Viscous dissipation and chemical reaction effects on MHD Casson nanofluid over a stretching sheet." Malaysian Journal of Fundamental and Applied Sciences 15, no. 4 (2019): 585–92. http://dx.doi.org/10.11113/mjfas.v15n4.1256.

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A numerical analysis was performed for the mathematical model of boundary layer flow of Casson nanofluids. Heat and mass transfer were analyzed for an incompressible electrically conducting fluid with viscous dissipations and chemical reaction past a stretching sheet. An appropriate set of similarity transformations were used to transform the governing partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is solved numerically by using shooting method. A detailed discussion on the effects of various physical parame
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Malarselvi, A., M. Bhuvaneswari, S. Sivasankaran, B. Ganga, and A. K. Abdul Hakeem. "Cross Diffusion Impacts on Chemically Reactive Unsteady Mass and Energy Transport Over Elongated Surface through Penetrable Medium." International Journal of Engineering & Technology 7, no. 4.10 (2018): 846. http://dx.doi.org/10.14419/ijet.v7i4.10.26773.

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The analysis of Dufour and Soret impacts on chemically reactive unsteady stream with molecules and energy transport in the thin fluid layer over an elongated surface rooted in a penetrable transporting agency with thermal suction/injection is scrutinized. The mathematically formulated PDEs are changed into ODEs with the application of similarity transforms. The converted ODEs are determined by Runge-Kutta method linked shooting process. Numerically computed data are graphically manifested to illustrate the domination of various parametric values. Numerical inspections are made over for local s
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Zwarycz-Makles, Katarzyna, and Dorota Majorkowska-Mech. "Gear and Runge–Kutta Numerical Discretization Methods in Differential Equations of Adsorption in Adsorption Heat Pump." Applied Sciences 8, no. 12 (2018): 2437. http://dx.doi.org/10.3390/app8122437.

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The main aim of this paper was to find the correct method of calculating equations of heat and mass transfer for the adsorption process and to calculate it numerically in reasonable time and with proper accuracy. An adsorption heat pump with a silica gel adsorbent and water adsorbate is discussed. We developed a mathematical model of temperature and uptake changes in the adsorber/desorber comprising the set of heat and mass balance partial differential equations (PDEs), together with the initial and boundary conditions and solved it by the numerical method of lines (NMOL). Spatial discretizati
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Arney, DavidC. "Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs." Computers & Chemistry 17, no. 3 (1993): 338–39. http://dx.doi.org/10.1016/0097-8485(93)80021-5.

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Dissertations / Theses on the topic "PDEs and ODEs numerical method"

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Tranquilli, Paul J. "Lightly-Implicit Methods for the Time Integration of Large Applications." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/81974.

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Many scientific and engineering applications require the solution of large systems of initial value problems arising from method of lines discretization of partial differential equations. For systems with widely varying time scales, or with complex physical dynamics, implicit time integration schemes are preferred due to their superior stability properties. However, for very large systems accurate solution of the implicit terms can be impractical. For this reason approximations are widely used in the implementation of such methods. The primary focus of this work is on the development of nov
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Montanelli, Hadrien. "Numerical algorithms for differential equations with periodicity." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:cc001282-4285-4ca2-ad06-31787b540c61.

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This thesis presents new numerical methods for solving differential equations with periodicity. Spectral methods for solving linear and nonlinear ODEs, linear ODE eigenvalue problems and linear time-dependent PDEs on a periodic interval are reviewed, and a novel approach for computing multiplication matrices is presented. Choreographies, periodic solutions of the n-body problem that share a common orbit, are computed for the first time to high accuracy using an algorithm based on approximation by trigonometric polynomials and optimization techniques with exact gradient and exact Hessian matrix
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Lee, Hock Seng, and n/a. "An ODE/MOL PDE Template For Soil Physics: A Numerical Study." Griffith University. Australian School of Environmental Studies, 2003. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20030616.142709.

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The aim of the thesis is to find a method, in conjunction with the ordinary differential equation (ODE) based method of lines (MOL) solution of Richards’ equation, to model the steep wetting front infiltration in very dry soils, accurately and efficiently. Due to the steep pressure head or steep water volumetric content gradients, highly nonlinear soil hydraulic properties and the rapid movement of the wetting front, accurate solutions for infiltration into a dry soil are usually difficult to obtain. Additionally, such problems often require very small time steps and large computation times. A
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Constantinescu, Emil Mihai. "Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/27938.

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Numerical simulation is necessary to understand natural phenomena, make assessments and predictions in various research and engineering fields, develop new technologies, etc. New algorithms are needed to take advantage of the increasing computational resources and utilize the emerging hardware and software infrastructure with maximum efficiency. Adaptive numerical discretization methods can accommodate problems with various physical, scale, and dynamic features by adjusting the resolution, order, and the type of method used to solve them. In applications that simulate real systems, the numeri
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Ugail, Hassan, N. Jamil, and R. Satinoianu. "Method of numerical simulation of stable structures of fluid membranes and vesicles." WSEAS, 2006. http://hdl.handle.net/10454/2751.

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Rockstroh, Parousia. "Boundary value problems for the Laplace equation on convex domains with analytic boundary." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/273939.

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In this thesis we study boundary value problems for the Laplace equation on do mains with smooth boundary. Central to our analysis is a relation, known as the global relation, that couples the boundary data for a given BVP. Previously, the global re lation has primarily been applied to elliptic PDEs defined on polygonal domains. In this thesis we extend the use of the global relation to domains with smooth boundary. This is done by introducing a new transform, denoted by F_p, that is an analogue of the Fourier transform on smooth convex curves. We show that the F_p-transform is a bounded and i
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Chen, Yung-Yu. "A Multi-Physics Software Framework on Hybrid Parallel Computing for High-Fidelity Solutions of Conservation Laws." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1313000975.

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Seguis, Jean-Charles. "A fictitious domain approach for hybrid simulations of eukaryotic chemotaxis." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:d56eae88-cb44-4c94-871f-3723347489a0.

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Chemotaxis, the phenomenon through which cells respond to external chemical signals, is one of the most important and universally observable in nature. It has been the object of considerable modelling effort in the last decades. The models for chemotaxis available in the literature cannot reconcile the dynamics of external chemical signals and the intracellular signalling pathways leading to the response of the cells. The reason is that models used for cells do not contain the distinction between the extracellular and intracellular domains. The work presented in this dissertation intends to re
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Nguyen, Dinh Liem. "Spectral Methods for Direct and Inverse Scattering from Periodic Structures." Phd thesis, Ecole Polytechnique X, 2012. http://tel.archives-ouvertes.fr/tel-00771746.

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The main topic of the thesis are inverse scattering problems of electromagnetic waves from periodic structures. We study first the direct problem and its numerical resolution using volume integral equation methods with a focus on the case of strongly singular integral operators and discontinuous coefficients. In a second investigation of the direct problem we study conditions on the material parameters under which well-posedness is ensured for all positive wave numbers. Such conditions exclude the existence of guided waves. The considered inverse scattering problem is related to shape identifi
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Auphan, Thomas. "Analyse de modèles pour ITER ; Traitement des conditions aux limites de systèmes modélisant le plasma de bord dans un tokamak." Phd thesis, Aix-Marseille Université, 2014. http://tel.archives-ouvertes.fr/tel-00977893.

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Cette thèse concerne l'étude des interactions entre le plasma et la paroi d'un réacteur à fusion nucléaire de type tokamak. L'objectif est de proposer des méthodes de résolution des systèmes d'équations issus de modèles de plasma de bord. Nous nous sommes intéressés au traitement de deux difficultés qui apparaissent lors de la résolution numérique de ces modèles. La première difficulté est liée à la forme complexe de la paroi du tokamak. Pour cela, il a été choisi d'utiliser des méthodes de pénalisation volumique. Des tests numériques de plusieurs méthodes de pénalisation ont été réalisés sur
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Books on the topic "PDEs and ODEs numerical method"

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D, Byrne George, Schiesser W. E, and American Institute of Chemical Engineers. Meeting, eds. Recent developments in numerical methods and software for ODEs/DAEs/PDEs. World Scientific, 1992.

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Byrne, G. D., and W. E. Schiesser. Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/1326.

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Griffiths, Graham W. Numerical Analysis Using R: Solutions to ODEs and PDEs. Cambridge University Press, 2016.

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Griffiths, Graham W. Numerical Analysis Using R: Solutions to ODEs and PDEs. Cambridge University Press, 2016.

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Griffiths, Graham W. Numerical Analysis Using R: Solutions to ODEs and PDEs. Cambridge University Press, 2016.

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Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator
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Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs. SIAM-Society for Industrial and Applied Mathematics, 2014.

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The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics). Society for Industrial and Applied Mathematic, 2006.

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Dahmen, W., and A. Reusken. Numerik für Ingenieure und Naturwissenschaftler (Springer-Lehrbuch). Springer, 2006.

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Numerik für Ingenieure und Naturwissenschaftler. Springer, 2006.

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Book chapters on the topic "PDEs and ODEs numerical method"

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Gerritsma, Marc, Artur Palha, Varun Jain, and Yi Zhang. "Mimetic Spectral Element Method for Anisotropic Diffusion." In Numerical Methods for PDEs. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94676-4_3.

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Bellen, A. "A Runge-Kutta-Nystrom Method for Delay Differential Equations." In Numerical Boundary Value ODEs. Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5160-6_16.

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Brown, David L. "A Numerical Method for Singular Perturbation Problems with Turning Points." In Numerical Boundary Value ODEs. Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5160-6_11.

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Markowich, Peter A. "A Finite Difference Method for the Basic Stationary Semiconductor Device Equations." In Numerical Boundary Value ODEs. Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5160-6_17.

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Maier, Maximilian R. "Numerical solution of singular perturbed boundary value problems using a collocation method with tension splines." In Numerical Boundary Value ODEs. Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5160-6_12.

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Neuberger, John M. "Review of Elementary Numerical Methods and MATLAB®." In Difference Matrices for ODE and PDE. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-12000-8_2.

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Castro, Carlos. "A Spectral Numerical Method to Approximate the Boundary Controllability of the Wave Equation with Variable Coefficients." In Research in PDEs and Related Fields. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-14268-0_3.

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Satyanarayana, Chirala. "RBF-FD Based Method of Lines with an Optimal Constant Shape Parameter for Unsteady PDEs." In Numerical Optimization in Engineering and Sciences. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-3215-3_26.

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Paszyński, Maciej, Rafał Grzeszczuk, David Pardo, and Leszek Demkowicz. "Deep Learning Driven Self-adaptive Hp Finite Element Method." In Computational Science – ICCS 2021. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-77961-0_11.

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AbstractThe finite element method (FEM) is a popular tool for solving engineering problems governed by Partial Differential Equations (PDEs). The accuracy of the numerical solution depends on the quality of the computational mesh. We consider the self-adaptive hp-FEM, which generates optimal mesh refinements and delivers exponential convergence of the numerical error with respect to the mesh size. Thus, it enables solving difficult engineering problems with the highest possible numerical accuracy. We replace the computationally expensive kernel of the refinement algorithm with a deep neural network in this work. The network learns how to optimally refine the elements and modify the orders of the polynomials. In this way, the deterministic algorithm is replaced by a neural network that selects similar quality refinements in a fraction of the time needed by the original algorithm.
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Łoś, Marcin, Robert Schaefer, and Maciej Smołka. "Effective Solution of Ill-Posed Inverse Problems with Stabilized Forward Solver." In Computational Science – ICCS 2021. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-77964-1_27.

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AbstractWe consider inverse parametric problems for elliptic variational PDEs. They are solved through the minimization of misfit functionals. Main difficulties encountered consist in the misfit multimodality and insensitivity as well as in the weak conditioning of the direct (forward) problem, that therefore requires stabilization. A complex multi-population memetic strategy hp-HMS combined with the Petrov-Galerkin method stabilized by the Demkowicz operator is proposed to overcome obstacles mentioned above. This paper delivers the theoretical motivation for the common inverse/forward error scaling, that can reduce significantly the computational cost of the whole strategy. A short illustrative numerical example is attached at the end of the paper.
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Conference papers on the topic "PDEs and ODEs numerical method"

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Gu, Jijun, Zhenhua Song, Kang Zhang, Liguo Su, and Menglan Duan. "Dynamic Response of a Fluid-Conveying Riser Subject to Vortex-Induced Vibration: Integral Transform Solution." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-24639.

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Analysis of dynamic response of a fluid-conveying riser is an important aspect in subsea production system. In the present paper, dynamic response of a pinned-pinned riser subject to external fluid force was solved by the generalized integral transform technique (GITT). A nonlinear wake oscillator models was used to represent the cross-flow and in-line force acting on the riser, leading to a coupled system of second-order Partial Differential Equations (PDEs). The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations (ODEs), which was numerically
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Lilley, David G. "Computational Methods Using Excel/VBA for Engineering Applications." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99172.

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The focus is that Excel/VBA provides a useful platform for engineering calculations in energy engineering. It includes computational methods in the simulation and solution of engineering problems that may or may not have analytical exact mathematical solutions. Emphasis is on the methods and applications, using Excel as the interface for data input and output, tables and figures, and Visual Basic for Applications VBA as the programming language for computations. Fundamental topics of: • Linear and Nonlinear Sets of Equations; • Interpolating Polynomials; • Differentiation and Integration; • So
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Singh, Munendra Pal, Md Emadur Rahman, and Suneet Singh. "Nodalized Reduced Ordered Model for Stability Analysis of Supercritical Fluid in Heated Channel." In ASME 2018 Power Conference collocated with the ASME 2018 12th International Conference on Energy Sustainability and the ASME 2018 Nuclear Forum. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/power2018-7366.

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In this paper, a novel nodalized reduced order model (NROM) has been developed to analyze the linear stability in a heated channel using supercritical water (SCW) as a coolant. The presented reduced order model is developed based on the two-phase flow system approach. The model is much simplified, which reduced the requirement of computational efforts and resources. In the heated channel, the SCW’s density shows a dramatic downfall near the pseudo-critical temperature, based on which it has been divided into n number of nodes. The one-dimension partial differentiation conservation equations of
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Zhang, Yuhong, and Sunil Agrawal. "A Lyapunov Controller for a Varying Length Flexible Cable System to Supress Transverse Vibration." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60269.

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Modeling and controller design for a flexible cable transporter system, with arbitrarily varying cable length is presented using Hamilton’s principle and Lyapunov theory. The axial velocity of the system is assumed to be arbitrary in the model. This is different from existing literature where the axial velocity is assumed either constant or is prescribed. The governing equations are coupled non-linear partial differential equations (PDEs) and ordinary differential equations (ODEs), and boundary conditions. The interactions between the cables and the slider, pulleys, and motors are included in
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Kakanda, Kabutakapua, Zhaolong Han, Bao Yan, Narakorn Srinil, and Dai Zhou. "A Novel Power Series Method for the Analysis of an Offshore Mooring Line." In ASME 2021 40th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/omae2021-63219.

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Abstract The mechanics of offshore mooring lines are described by a set of nonlinear equations of motion which have typically been solved through a numerical finite element or finite difference method (FEM or FDM), and through the lumped mass method (LMM). The mooring line nonlinearities are associated with the distributed drag forces depending on the relative velocities of the environmental flow and the structure, as well as the axial dynamic strain-displacement relationship given by the geometric compatibility condition of the flexible mooring line. In this study, a semi analytical-numerical
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Rastgoftar, Hossein, Mehrdad Gharib Shirangi, and Mohammad Eghtesad. "Boundary Control of Temperature Distribution in a Rectangular FGM Plate." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12081.

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In this paper an analytical method and a PDE-based solution to control temperature distribution in FGM plates is introduced. For the rectangular FGM plate under consideration, it is assumed that the material properties such as thermal conductivity, density, and specific heat capacity, vary in the width direction (y); and the governing heat conduction equation of the plate is a second-order partial differential equation. Since there has been little control synthesis work for PDE-based systems as compared to the abundance of control design techniques available for ordinary differential equations
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Vyasarayani, Chandrika P., Eihab M. Abdel-Rahman, John McPhee, and Stephen Birkett. "Modelling MEMS Resonators Past Pull-In." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67763.

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In this paper, we develop a mathematical model of an electrostatic MEMS beam undergoing impact with a stationary electrode subsequent to pull-in. We model the contact between the beam and the substrate using a nonlinear foundation of springs and dampers. The system partial differential equation (PDE) is converted into coupled nonlinear ordinary differential equations (ODEs) using the Galerkin method. A numerical solution is obtained by treating all nonlinear terms as external forces.
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Namala, Sundar, and Rizwan Uddin. "Hybrid Nodal Integral/Finite Element Method (NI-FEM) for Time-Dependent Convection Diffusion Equation." In 2020 International Conference on Nuclear Engineering collocated with the ASME 2020 Power Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/icone2020-16703.

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Abstract Nodal integral methods (NIM) are a class of efficient coarse mesh method that use transverse averaging to reduce the governing partial differential equation(s) (PDE) into a set of ordinary differential equations (ODE), and these ODEs or their approximations are analytically solved. Since this method depends on transverse averaging, the standard application of this approach gets restricted to domains that have boundaries that are parallel to one of the coordinate axes (2D) or coordinate planes (3D). The hybrid nodal-integral/finite-element method (NI-FEM) has been developed to extend t
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Caruntu, Dumitru I., Julio S. Beatriz, and Christian Reyes. "Electrostatically Actuated M/NEMS With Casimir Effect: Primary Resonance — Comparison Between Three Methods." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67218.

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Abstract:
This paper deals with electrostatically actuated micro- and nano-electromechanical systems (M/NEMS) cantilever resonator under electrostatic actuation. The model includes Casimir effect. Three different methods are used to investigate the primary resonance of the MEMS resonator. The first two methods are based on a Galerkin approach in which the initial value and boundary value problem, given by the partial differential equation (PDE) of motion and the initial and boundary conditions, is transformed into an initial value problem of one ordinary differential equation (ODE) or a system of ODEs d
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Houbak-Jensen, Lars, Anders Holten, Morten Boje Blarke, Eckhard A. Groll, Ali Shakouri, and Kazuaki Yazawa. "Dynamic Analysis of a Dual-Mode CO2 Heat Pump With Both Hot and Cold Thermal Storage." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62894.

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We investigated the dynamics of a transcritical CO2 heat pump system including hot and cold thermal storages, which makes up the concept “thermal battery”. The analytical model is used for the study of the dynamics of the system involving simultaneous supply of heating and cooling for buildings. The model includes the dynamics of the gas cooler, evaporator and the thermal storages, while the compressor and the expansion valve are considered quasi-static. The heat transfer in the dynamically modeled components is described by partial differential equations (PDEs) consisting of heat conduction,
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Reports on the topic "PDEs and ODEs numerical method"

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X. Frank Xu. Numerical Stochastic Homogenization Method and Multiscale Stochastic Finite Element Method - A Paradigm for Multiscale Computation of Stochastic PDEs. Office of Scientific and Technical Information (OSTI), 2010. http://dx.doi.org/10.2172/1036255.

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