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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.

In this paper, we are concerned with the problem of applying cubic non-polynomial spline functions to develop a numerical method for obtaining approximation for the solution for cubic nonlinear Schrodinger equation. The truncation error of the method is theoretically analyzed. Using the Von Neumann method, the proposed method is shown to be unconditionally stable. The linearization technique is carried out to solve the system and to prove that the method is unconditionally stable. Two numerical examples are included to illustrate the practical implementation of the proposed method.

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.