A second-order accurate difference scheme for an extended Fisher–Kolmogorov equation

In this paper, we present a Crank–Nicolson type finite difference scheme to approximate the nonlinear evolutionary Extended Fisher–Kolmogorov (EFK) equation. We prove the existence of the solution by using the well-known Browder fixed-point theorem. The stability of this scheme is established in L∞L∞-norm. The uniqueness and convergence of the solution are analyzed. We discuss an iterative algorithm for solving the difference scheme and prove its convergence.