A Generalized Chebyshev Method for Non-linear Parabolic Equations in One Space Variable

Publisher Website
Google Scholar
Abstract
The derivation and implementation of a generalized Chebyshev method is described for the numerical solution of non-linear parabolic equations in one space dimension. The solution is obtained by using the method of lines and is approximated in the space variable by piecewise Chebyshev polynomial expansions. These expansions are normally few in number and of high order. It is shown that the method can be derived from a perturbed form of the original equation. A numerical example is given to illustrate its performance compared with the finite element and finite difference method. A comparison of various Chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

This publication has 0 references indexed in Scilit: