A unified approach to the Tau Method and Chebyshev series expansion techniques

Abstract In this paper, we show the full equivalence between the recursive [1] and operational [2] formulations of the Tau Method. We then use such methods as analytic tools in the simulation of other numerical techniques for the approximate solution of differential equations, as Tau Methods with special perturbation terms. In this paper, we consider, as examples of this approach, two classical numerical techniques based on Chebyshev series expansions. We introduce a numerical parameter, the length of a method, to compare different numerical techniques with reference to a given basis. Our results make possible the recursive formulation of a variety of series expansion methods.