An Efficient High-Order Algorithm for Solving Systems of Reaction-Diffusion Equations
Document Type
Article
Publication Date
2002
Publication Title
Numerical Methods for Partial Differential Equations
Abstract
An efficient higher-order finite difference algorithm is presented in this article for solving systems of two-dimensional reaction-diffusion equations with nonlinear reaction terms. The method is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular five-point difference stencil similar to that used in the standard second-order algorithm, such as the Crank-Nicolson algorithm. The Padé approximation and Richardson extrapolation are used to achieve high-order accuracy in the spatial and temporal dimensions, respectively. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.
Repository Citation
Liao, W., Zhu, J., and Khaliq, A. Q. M. (2002). An Efficient High-order Algorithm for Solving Systems of Reaction-diffusion Equations. Journal of Numerical Methods for Partial Differential Equations, 18(3), 340 - 354, doi: 10.1002/num.10012.
Original Citation
Liao, W., Zhu, J., and Khaliq, A. Q. M. (2002). An Efficient High-order Algorithm for Solving Systems of Reaction-diffusion Equations. Journal of Numerical Methods for Partial Differential Equations, 18(3), 340 - 354, doi: 10.1002/num.10012.
DOI
10.1002/num.10012
Publisher's Statement
The definitive version is available at www3.interscience.wiley.com
Volume
18
Issue
3
