Numerical studies of the cubic non-linear Schrodinger equation

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 non-linear 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.