The Pseudo-spectral Method and Matlab Implement

摘要

The pseudo-spectral method based on function approach was good for solving nonlinear equation. Matlab can solve many complicated engineering problem, and the numerical results can be showed by its excellent graphics. It is convenience to program with the Matlab for PS method. The PS method used Fourier transform treatment of the space dependence together with a leapfrog scheme in time, in the paper, the traditional Lax-Wendroff form is discarded, and the PS method is adopted. We adopt the averages of adjacent levels and restart the scheme from the new levels for the possibility of separation of the solutions between successive time levels. And the complex-valued problem in Fourier transform is treated. Taking an example, the fKdV equation is calculated, and draws the waterfall with Matlab.