THE SOLUTION OF NONLINEAR SCHRODINGER-EQUATIONS USING ORTHOGONAL SPLINE COLLOCATION

An orthogonal spline collocation semidiscretization, previously applie d in the numerical solution of the cubic Schrodinger equation, is exte nded to the solution of Schrodinger equations which possess general po wer nonlinearities and nonlinear terms that contain derivatives. The a ccuracy of the method is examined, as well as its ability to conserve approximations to certain invariants associated with the theoretical s olution. The results of numerical experiments are presented in which t he integration in time is performed using a routine from a software li brary. Particular attention is paid to the value and limitations of co nservation as an indicator of accuracy.