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An Efficient High-Order Algorithm for Solving Systems of Reaction-Diffusion Equations
Numerical Methods for Partial Differential Equations
  • Wenyuan Liao, Mississippi State University
  • Jianping Zhu, Cleveland State University
  • Abdul Q.M. Khaliq, Middle Tennessee State University
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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.

Citation Information
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.