The local discontinuous Galerkin method for Burger's-Huxley and Burger's-Fisher equations

In this paper, a numerical solution for the generalized Burger's-Huxley equation and the generalized Burger's-Fisher equation are presented by using the local discontinuous Galerkin method. Firstly we rewrite the two kinds of equations into first order systems, then apply the discontinuous Galerkin method to the systems. Secondly, the systems for ordinary differential equations yielded are solved by the third-order Runge-Kutta time integration method. The numerical results obtained by this way are compared with exact solution to demonstrate accuracy and capability of the method.