Numerical Solution of Coupled Burgers' Equation Using Finite Difference and Sinc Collocation Method

This paper is concerned with numerical solution of coupled Burgers' equation by the combination of finite difference and sinc collocation method. Firstly, we derive the semi discrete scheme by approximating the first order derivative of time with theta-weighted scheme. Different schemes can be obtained by selecting different values of theta. After that, a fully discrete scheme is constructed through the use of sinc collocation and finite difference method to approximate the first and second order derivatives of space. The stability of the fully discrete scheme is analyzed by representing the proposed scheme in matrix form. For Burgers' equation, the similar results could be obtained. At last, some numerical examples are presented to illustrate the efficiency and superiority of present method for solving Burgers' and coupled Burgers' equation.