A leapfrog algorithm and stability studies for the non-linear Schrodinger equation

الملخص EN

A B-spline finite element method is applied to the solution of the non-linear Schrodinger equation.

The approach used is based on collocation of cubic B-splines over spatial finite elements, so that we have continuity of the dependent variable and its first two derivatives throughout the solution range, and a leapfrog approximation in time.

Stability of the numerical algorithm is discussed and standard problems studied.

The algorithm has good conservation properties and does not suffer from non-linear blowup.

Comparisons are made with published numeric and analytic solutions.