A LEAPFROG ALGORITHM AND STABILITY STUDIES FOR THE NONLINEAR SCHRODINGER-EQUATION

A B-spline finite element method is applied to the solution of the non -linear Schrodinger equation. The approach used is based on collocatio n of cubic B-splines over spatial finite elements, so that we have con tinuity of the dependent variable and its first two derivatives throug hout the solution range, and a leapfrog approximation in time. Stabili ty of the numerical algorithm is discussed and standard problems studi ed. The algorithm has good conservation properties and does not suffer from non-linear blowup. Comparisons are made with published numeric a nd analytic solutions.