Parallel implementation of the split-step and the pseudospectral methods for solving higher KdV equation

Abstract

Numerical simulations show that higher order KdV equation under certain conditions has a self-focusing singularity, which means that the solution of the equation blows up in finite time. In this paper, two numerical schemes: the split-step Fourier transform and the pseudospectral methods are used to investigate this self-focusing singularity problem. Parallel algorithms for the proposed schemes are designed and implemented. FFTW-MPI algorithm designed by Matteo Frigo and Steven Johnson is used for parallel implementation of the discrete Fourier transform (DFT). The parallel algorithms are implemented on an SGI Origin 2000 multiprocessor computer and experiments show that a considerable speedup is attained.