Pseudospectral and Galerkin Methods

Abstract

Wave equations have been successfully discretized using all of the standard families of algorithms: finite difference, finite element, and spectral. Nevertheless, this volume will review only Chebyshev and Fourier spectral methods.

“It is said that in a certain grassy part of the world a man will walk a mile to catch a horse, whereon to ride a quarter of a mile to pay an afternoon call. Similarly, it is not quite respectable to arrive at a mathematical destination, under the gaze of a learned society, at the mere footpace of arithmetic. Even at the expense of considerable time and effort, one should be mounted on the swift steed of symbolic analysis. ” — Lewis F. Richardson, in “How to solve differential equations ap–proximately by arithmetic.” Math. Gazette, 12, 415-421 (1925), reprinted in his Collected Works.