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

Tang, S.; Qin, S.; Weber, R. O.

J. Aust. Math. Soc., Ser. B 35, No. 2, 223-243 (1993).

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.

Reviewer: J.Vaníček (Praha)

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

Keywords:

numerical study; explicit finite difference method; Petrov-Galerkin finite element method; reaction-diffusion equation; quasitravelling waves; long time behaviour