Parametric cubic spline method for the solution of the nonlinear Schrödinger equation

In this work, we present a numerical method based on parametric cubic splines for solving the cubic nonlinear Schrödinger equation. The truncation error is given and it has been shown that by choosing suitable parameters we can obtain various accuracy schemes. Stability analysis of the method based on the von Neumann technique has been carried out and the method is shown to be unconditionally stable. The efficiency of the method is demonstrated by test problems. The lowest two conserved quantities are computed. The numerical simulations validate and demonstrate the advantages of the method.