The differential quadrature solution of nonlinear reaction-diffusion and wave equations using several time-integration schemes

Date

2011-04-01

Author

Meral, Gulnihal
Tezer, Münevver

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Three different time-integration schemes, namely the finite difference method (FDM) with a relaxation parameter, the least-squares method (LSM) and the finite element method (FEM), are applied to the differential quadrature (DQM) solution of one-dimensional nonlinear reaction-diffusion and wave equations. In the solution procedure, the space derivatives are discretized using DQM, which may also be used without the need of boundary conditions. The aim of the paper is to find computationally more efficient time-integration algorithm by comparison. For the nonlinear reaction-diffusion equation, which is a parabolic type, FEM is found to be the method of choice in terms of accuracy and computational cost. For the nonlinear wave equation, it is seen that both the FDM and LSM are better than FEM. Therefore, LSM can be preferred as a direct method for the nonlinear wave equation. Copyright (C) 2009 John Wiley & Sons, Ltd.

Subject Keywords

Modelling and Simulation, Computational Theory and Mathematics, Software, Applied Mathematics, Molecular Biology, Biomedical Engineering

URI

https://hdl.handle.net/11511/35538

Journal

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING

DOI

https://doi.org/10.1002/cnm.1305

Collections

Department of Mathematics, Article

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Citation Formats

G. Meral and M. Tezer, “The differential quadrature solution of nonlinear reaction-diffusion and wave equations using several time-integration schemes,” INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, pp. 485–497, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35538.