On the performance of some NSFD methods for a 2-D generalized Burgers–Huxley equation

Abstract

In this work, we construct four finite difference schemes in order to discretize a 2-D generalized Burgers–Huxley equation. Two explicit non-standard finite difference methods are initially proposed and termed as NSFD1 and NSFD2. To improve the results, a modification to NSFD1 is made using the technique of remainder effect, scheme is termed as NSFD3 and an implicit non-standard finite difference is also constructed. We considered three different regimes for the parameters controlling advection, diffusion and reaction in other to test efficacy of the methods. The performance of the four methods is compared by computing absolute errors, relative errors, L and L errors and CPU time. All the four schemes constructed are novel and the derivation of time-splitting non-standard finite difference methods is not very common.