Compact Finite Difference Scheme Combined with Richardson Extrapolation for Fisher’s Equation

Abstract

In this study, the fourth-order compact finite difference scheme combined with Richardson extrapolation for solving the 1D Fisher’s equation is presented. First, the derivative involving the space variable is discretized by the fourth-order compact finite difference method. Then, the nonlinear term is linearized by the lagging method, and the derivative involving the temporal variable is discretized by the Crank–Nicolson scheme. The method is found to be unconditionally stable and fourth-order accurate in the direction of the space variable and second-order accurate in the direction of the temporal variable. When combined with the Richardson extrapolation, the order of the method is improved from fourth to sixth-order accurate in the direction of the space variable. The numerical results displayed in figures and tables show that the proposed method is efficient, accurate, and a good candidate for solving the 1D Fisher’s equation.