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An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations. (English) Zbl 1019.65065

Summary: We discuss an efficient higher order finite difference algorithm for solving systems of 3-D reaction–diffusion equations with nonlinear reaction terms. The algorithm is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular seven-point difference stencil similar to that used in the standard second-order algorithms, such as the Crank–Nicolson algorithm. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
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