Parallel calculation of differential quadrature method for the burgers-huxley equation

Abstract

In this study, the Burgers-Huxley equation with Dirichlet?s boundary conditions is treated by the Differential Quadrature method (DQM). The different types of grid points spacing used in the DQM, which is the equally-spaced and the Chebychev-Gauss-Lobatto grid points have been investigated on their effect on the accuracy of results generated. The finite difference method (FDM) will be used to solve some examples of Burgers-Huxley equation in order to compare with the solutions obtained by DQM to show the stability and accuracy of the numerical method. Then, the set of ordinary differential equations obtained is solved by using different types of implicit Runge-Kutta (RK) methods. C language programmes have been developed based on the examples discussed. Also, shared memory architecture of parallel computing is done by using OpenMP in order to reduce the time taken in simulating the numerical results. Consequently, the results showed that the Differential Quadrature method is a good alternative in approximating the Burgers-Huxley equation with excellent accuracy and stability.