Error analysis of the Tau Method: Dependence of the error on the degree and on the length of the interval of approximation

Abstract In this paper, we discuss the dependence of Tau Method approximations on (i) the degree of approximant n and (ii) the length of the interval of approximation h . We shall show that the Tau Method parameters τ i (i) decay exponentially in terms of n and (ii) for a fixed n they decay in terms of h as ( h /2) n .