Application of linear combination between cubic B-spline collocation methods with different basis for solving the KdV equation

Document Type : Research Paper


1 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City (11884), Cairo, Egypt

2 Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt


In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using a new approach by combining cubic B-spline functions. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms L2, L∞ are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply.