AN h-p VERSION OF THE CHEBYSHEV SPECTRAL COLLOCATION METHOD FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH VANISHING DELAYS

摘要

We propose a spectral collocation method based on the Chebyshev-Gauss-Lobatto points for linear Volterra integro-differential equations with vanishing delays. We derive an h - p version a-priori error estimate in the H-1-norm that is completely explicit in the local time steps and the local polynomial degrees. Numerical experiments are provided to confirm the theoretical results.