Upper and lower error estimation for the Tau method: Some remarks on a problem of rational approximation

Abstract

We show that an error analysis of Y.L. Luke for a rational Tau Method approximation of the solution of the first order differential equation with constant coefficients, a technique due to G. Meinardus and a new relation between Legendre and Bernstein polynomials we give in this paper, can be combined to give upper and lower error bounds for the error vector of a Tau Method rational approximation of a system of ordinary differential equation with constant coefficients.