Numerical Solution of the Generalized Burgers-Huxley Equation by Exponential Time Differencing Scheme

Numerical solutions of nonlinear partial differential equations, such as the generalized and extended Burgers-Huxley equations which combine effects of advection, diffusion, dispersion and nonlinear transfer are considered in this paper. Such system can be divided into linear and nonlinear parts, which allow the use of two numerical approaches. Higher order finite difference schemes are employed for the spatial discretization, the resulting nonlinear system of ordinary differential equation is advanced with the modified fourth-order exponential time differencing Runge-Kutta (ETDRK4) method designed to generate the scheme with a smaller truncation error and better stability properties. The stability region of this scheme is shown and computed via its amplification factor. Numerical simulations with comparisons are presented to address any queries that may arise.