The Open Applied Mathematics Journal

2007, 1 : 15-20
Published online 2007 October 17. DOI: 10.2174/1874114200701010015
Publisher ID: TOAMJ-1-15

Application of the Non-Polynomial Spline Approach to the Solution of the Burgers’ Equation

Mohamed A. Ramadan , Talaat S. El-Danaf and Faisal E.I. Abd Alaal
Department of Mathematics, Faculty of Science, Menoufia University, Shebeen El-Koom, Egypt.

ABSTRACT

In this paper, we propose a non-polynomial spline based method to develop a numerical method for approximation to the Burgers’ equation. Applying the Von-Neumann stability analysis, we show that the proposed method is unconditionally stable. A numerical example is given to illustrate the applicability and the accuracy of the presented new method.

Keywords:

Non-polynomial spline, nonlinear burgers’ equation, von neumann stability, accuracy.