Implicit spectral methods for wave propagation problems (Q1181873)

The numerical solution of a nonlinear wave equation can be obtained by using spectral methods to resolve the unknown in space and the Crank- Nicolson scheme to advance the solution in time. The authors analyze iterative techniques for solving the nonlinear equations that arise from such implicit time-stepping schemes for the Korteweg-de Vries and the Kadomtsev-Petviashvili equations. They derive predictor-corrector methods that retain the full accuracy of the implicit method with minimal stability restrictions on the size of the time step. The efficiency of such a method is demonstrated by some numerical examples.