Some numerical experiments on fisher equation

Abstract Fisher's equation which represents a reactive-diffusive system and has an exact traveling wave solution is used to compare several finite-differennce schemes. Iterative implicit, quasi-linear implicit, predictor-corrector explicit, and two forms of operator-splitting formulations have been examined. A stiffness parameter is introduced in the reaction term to vary the stiffness of the Fisher's equation. The numerical methods are compared on the basis of effectiveness curves. The results indicate that the time-linearization method is superior to the quasi-linearization method, that the Crank-Nicolson formulation is better than the standard implicit formulation, that the predictor-corrector explicit method is more effective than the Crank-Nicolson implicit method, that the two-step operator-splitting method is superior to the one-step operator-splitting method, and that the two-step operator-splitting with a fourth-order accurate solver for the reaction term is the most effective method.