Numerical solution of the one-dimensional Burgersa€? equation: Implicit and fully implicit exponential finite difference methods

摘要

This paper describes two new techniques which give improved exponential finite difference solutions of Burgersa€? equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgersa€? equation. As the Burgersa€? equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newtona€?s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.