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Numerical studies on 2-dimensional reaction-diffusion equations. (English) Zbl 0807.65103

The authors compare the explicit finite difference method, the Galerkin and the Petrov-Galerkin finite element method for the numerical solution of various initial and boundary value problems for a 2-dimensional reaction-diffusion equation. The results show the behaviour of the transition processes from different local initial disturbances to quasitravelling waves and also demonstrate the long time behaviour of the solutions, which is determined by the system itself and does not depend on the details of the initial disturbances.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
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