IMPLICIT SPECTRAL METHODS FOR WAVE-PROPAGATION PROBLEMS

The numerical solution of a non-linear wave equation can be obtained by using spectral methods to resolve the unknown in space and the standard Crank-Nicolson differencing scheme to advance the solution in time. We have analyzed iterative techniques for solving the non-linear equations that arise from such implicit time-stepping schemes for the K-dV and the KP equations. We derived predictor-corrector method that retain the full accuracy of the implicit method with minimal stability restrictions on the size of the time step. Some numerical examples show the propagation of interacting solitons. © 1991.