An Improved Method for the Solution of the Heat Equation in Chebyshev Series

A method is given for the numerical solution of the heat equationusing Chebyshev series. A feature of the method is that thematrices which have to be inverted (apart possibly from a few22 matrices) are all triangular. The method shows a considerableimprovement in accuracy over previous Chebyshev methods, particularlyas far as the approximation to the fundamental eigenvalue isconcerned. The extension of the method to equations of the form is also described.