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

Abstract

a b s t r a c tIn 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 ∞ -norm. The uniqueness and convergence of the solution are analyzed. We discuss an iterative algorithm for solving the difference scheme and prove its convergence.

An efficient numerical simulation of nonlinear‐dispersive model of shallow water wave

“…A high-order conservative difference scheme for nonlinear PDE's has been studied in [26][27][28][29][30][31][32][33].…”

Gegenbauer wavelet collocation method for the extended Fisher‐Kolmogorov equation in two dimensions

“…They also studied finite element Galerkin method for the two‐dimensional EFK equation and optimal error estimates in Danumjaya and Pani . Kadri and Omrani investigated Crank‐Nicolson–type finite difference scheme and nonlinear high‐order difference scheme to approximate the nonlinear evolutionary EFK equation. Khiari and Omrani derived finite difference scheme for the EFK equation in two dimensions.…”

A fourth‐order H1‐Galerkin mixed finite element method for Kuramoto–Sivashinsky equation

“…Further, using C 1 -conforming finite element method, optimal error estimates are established in Danumjaya et al [14], for both the semi-discrete and fully discrete cases for the extended Fisher-Kolmogorov equation in two-space dimension. A Crank-Nicholson type finite difference scheme to approximate the extended Fisher-Kolmogorov equation is presented and the existence and uniqueness of the solution are discussed in Kadri et al [15]. Further, existence, uniqueness, and convergence of Crank-Nicholson type finite difference solutions are discussed for the extended Fisher-Kolmogorov (EFK) equation in two-space dimension in Khiari et al [16].…”