The computational efficiency of a spectral walsh function method

Abstract

This paper examines the computational efficiency of the new fully discrete versions of the Walsh function spectral method due to Blyth. Following an introduction to the Walsh functions and relevant properties, ways of obtaining a fully discrete spectral Walsh function method are examined. The efficiency of the spectral method is compared with well-known standard schemes where a variable coefficient one-dimensional wave equation is used as the model problem. Some properties, such as how errors increase as t increases, for various t discretized versions of this scheme, are compared.