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.
An Efficient High-Order Algorithm for Solving Systems of Reaction-Diffusion EquationsNumerical Methods for Partial Differential Equations
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Citation InformationLiao, 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.