Chebyshev Methods for the Numerical Solution of Parabolic Partial Differential Equations in Two and Three Space Variables

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Abstract
Chebyshev methods for the numerical solution of parabolic partial differential equations in a region which can be transformed to either a square or a circular cylinder are developed. These procedures are an extension of the method of Knibb & Scraton (1971). To illustrate the technique the solution of the heat conduction equation within an elliptical region is considered in detail. The Chebyshev method given for this problem requires considerably less computer time than the method of Dew & Scraton (1973). In the case when the space operators commute a highly efficient alternating direction Chebyshev method is given.