A new three-level fourth-order compact finite difference scheme for the extended Fisher-Kolmogorov equation

Abstract

In this paper, a new fourth-order compact finite difference scheme is proposed to solve the extended Fisher-Kolmogorov (EFK) equation. The scheme is three-level and implicit nonlinear. A new time discretization technique is adopted in the new scheme. The priori estimate and convergence of the numerical solution are obtained by using the discrete energy method, and the optimal error estimation in the maximum norm shows that the proposed numerical scheme has second-order accuracy in time and fourth-order accuracy in space. Finally, the theoretical analysis is supported by the numerical results of several examples.