Numerical and parallel algorithms for the CMKdV equation

Abstract

This thesis is concerned with numerical and parallel algorithms for the complex modified Korteweg-de Vries (CMKdV) equation. It is composed of two parts. The first part deals with the split-step Fourier methods for this equation. Five different numerical schemes are studied. We first present those schemes. Then implementations of those schemes for the numerical simulation are carried out and numerical results are reported. In the second part of this thesis, we develop the parallel algorithms for these five schemes and implement them on the Origin 2000 multiprocessor computer. Speedup is tested.