Upper and lower error estimation for the Tau Method and related polynomial techniques

AbstractA new method is discussed by which estimates of upper and lower bounds of the maximum Tau Method approximation error are obtained. It improves on the upper bound estimate of Lanczos and other more recently proposed estimates. We give an example of a non-linear Ode where our technique is applied and show how it is implemented for Chebyshev series expansions, collocation and spectral methods