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

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

233
views

0
downloads

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

Suggestions

OpenMETU
Core

The comparison between the DRBEM and DQM solution of nonlinear reaction-diffusion equation MERAL, GÜLNİHAL; Tezer, Münevver (Elsevier BV, 2011-10-01) In this study, both the dual reciprocity boundary element method and the differential quadrature method are used to discretize spatially, initial and boundary value problems defined by single and system of nonlinear reaction-diffusion equations. The aim is to compare boundary only and a domain discretization method in terms of accuracy of solutions and computational cost. As the time integration scheme, the finite element method is used achieving solution in terms of time block with considerably large time ...
The DRBEM solution of incompressible MHD flow equations Bozkaya, Nuray; Tezer, Münevver (Wiley, 2011-12-10) This paper presents a dual reciprocity boundary element method (DRBEM) formulation coupled with an implicit backward difference time integration scheme for the solution of the incompressible magnetohydrodynamic (MHD) flow equations. The governing equations are the coupled system of Navier-Stokes equations and Maxwell's equations of electromagnetics through Ohm's law. We are concerned with a stream function-vorticity-magnetic induction-current density formulation of the full MHD equations in 2D. The stream f...
Differential quadrature solution of nonlinear reaction-diffusion equation with relaxation-type time integration Meral, G.; Tezer, Münevver (Informa UK Limited, 2009-01-01) This paper presents the combined application of differential quadrature method (DQM) and finite-difference method (FDM) with a relaxation parameter to nonlinear reaction-diffusion equation in one and two dimensions. The polynomial-based DQM is employed to discretize the spatial partial derivatives by using Gauss-Chebyshev-Lobatto points. The resulting system of ordinary differential equations is solved, discretizating the time derivative by an explicit FDM. A relaxation parameter is used to position the sol...
Fundamental solution for coupled magnetohydrodynamic flow equations Bozkaya, Canan; Tezer, Münevver (Elsevier BV, 2007-06-01) In this paper, a fundamental solution for the coupled convection-diffusion type equations is derived. The boundary element method (BEM) application then, is established with this fundamental solution, for solving the coupled equations of steady magnetohydrodynamic (MHD) duct flow in the presence of an external oblique magnetic field. Thus, it is possible to solve MHD duct flow problems with the most general form of wall conductivities and for large values of Hartmann number. The results for velocity and ind...
Computational modeling of passive myocardium Göktepe, Serdar; Wong, Jonathan; Kuhl, Ellen (Wiley, 2011-01-01) This work deals with the computational modeling of passive myocardial tissue within the framework ofmixed, non-linear finite element methods. We consider a recently proposed, convex, anisotropic hyperelastic model that accounts for the locally orthotropic micro-structure of cardiac muscle. A coordinate-free representation of anisotropy is incorporated through physically relevant invariants of the Cauchy-Green deformation tensors and structural tensors of the corresponding material symmetry group. This model...

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.