Higher-order compact finite difference method for systems of reaction-diffusion equations. (English) Zbl 1185.65154
The Dirichlet problem for a semilinear spatially two-dimensional system of reaction-diffusion equations is considered. The authors propose and analyze a compact difference scheme for existence and uniqueness of solution, furthermore for convergence properties of three iterative procedures for solving the discretized system. The scheme, being fourth-order in space and second-order in time is modified by Richardson extrapolation to fourth-order in time as well.
Numerical results for applications to an enzyme-substrate reaction-diffusion problem are displayed.
Numerical results for applications to an enzyme-substrate reaction-diffusion problem are displayed.
Reviewer: S. Burys (Kraków)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35K57 | Reaction-diffusion equations |
Keywords:
system of reaction-diffusion equations; compact finite difference method; higher-order accuracy; monotone iterations; upper and lower solutionsReferences:
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