Parallel Spectral Numerical Methods
Parallel Spectral Numerical Methods starts by taking a quick look at finite precision arithmetic. It then discusses how to solve ordinary differential equations (ODE) and partial differential equations (PDE) using separation of variables. Next, it introduces numerical time-stepping schemes that can be used to solve ODEs and PDEs. This is followed by an introduction to pseudo spectral methods through an overview of the discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT) algorithm that is used to quickly calculate the DFT. Finally it will combine all of these to solve a couple of different PDEs first in a serial setting and then in a parallel setting.
The programs will use Matlab and Fortran. A Python implementation of some of the Matlab programs is also provided.