An Exponential Finite Difference Method Based on Padé Approximation

Abstract

This paper reports a new technique of forming improved exponential finite difference solution of the one dimensional Burgers' equation.  The technique is called explicit exponential finite difference method based on Padé approximation. The main purpose of the paper is improve the exponential finite difference method and define an alternative method for the solution of the Burgers' equation. The advantage of the present method is reduced the computation cost to other exponential methods for solving the Burgers' equation. Accuracy of the present method is demonstrated by solving test problems and comparing numerical results with exact solution for different values of Reynolds' number.

Keywords

• Burgers' equation,Exponential finite difference method,Explicit exponential finite difference method,Finite difference methods,Padé approximation

References

1. Abassy, T.A; El-Tawil, M.A; El-Zoheiry H. Exact Solutions of Some Nonlinear Partial Differential Equations Using the Variational Iteration Method Linked with Laplace Transforms and the Padé Technique. Computers and Mathematics with Applications. 2007; 54, 940-954.