Operator compact method of accuracy two in time and four in space for the solution of time dependent Burgers-Huxley equation

Abstract

In this paper, we propose a new two-level implicit compact operator method of order two in time (t) and four in space (x) for the solution of time dependent Burgers-Huxley equation with appropriate initial and boundary conditions. The presence of Reynolds number and nonlinear terms in the problem leads to severe difficulties in the numerical approximation. To overcome such difficulties, the method based on operators is constructed. We use only 3-spatial grid points and the obtained tridiagonal nonlinear system has been solved by Newton's iteration method. The test problems considered in the literature have been discussed to demonstrate the strength and utility of the proposed method. The computed numerical solutions are in good agreement with the exact solutions. We show that the proposed method enables us to obtain high accuracy solution for high Reynolds number.