Singularly perturbed Burger-Huxley equation: Analytical solution through iteration

Abstract

The work presented considers the initial boundary value problem for nonlinear singularly perturbed time dependent Burger- Huxley equation. The equation contains two terms with nonlinearities, the cubic term and the advection term. Generally, the severe difficulties of two types encounter in solving this problem. The first one comes from these nonlinearity terms and the second is due to the perturbation parameter in the diffusion term. When the perturbation parameter approaches zero, the problem exhibit boundary layers and most of conventional methods fails to capture this effect. A relatively different analytical technique called variational iteration method (VIM), is used to solve this equation. This method is able to obtain rapidly convergent successive approximations of exact solution without any restrictive approximations or the transformations that may change the physical behaviour of the problem. Numerical examples are studied to demonstrate the significance and effect of various parameters involved in the equation.

Keywords: Burger-Huxley equation, iteration method, analytical solution, nonlinearity, singularly perturbed, advection