Chebyshev Methods for Ordinary Differential Equations

Abstract

The solution of linear ordinary differential systems, with polynomial coefficients, can be approximated by a finite polynomial or a finite Chebyshev series. The computation can be performed so that the solution satisfies exactly a perturbed differential system, the perturbations being computed multiples of one or more Chebyshev polynomials. An upper bound to the errors in the solution can often be estimated by approximate solution of the differential system satisfied by the error. Various devices are used to make the errors smaller, including a priori integration of the given differential various aspects of these topics, for both initial-value and boundary-value problems, and also suggests a method for automatic computation.