Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions

The theory of a class of spectral methods is extended to Volterra integro-differential equations which contain a weakly singular kernel ( t - s )->* with 0 1. In this work, we consider the case when the underlying solutions of weakly singular Volterra integro-differential equations are sufficiently smooth. We provide a rigorous error analysis for the spectral methods, which shows that both the errors of approximate solutions and the errors of approximate derivatives of the solutions decay exponentially in L °°-norm and weighted L 2 -norm. The numerical examples are given to illustrate the theoretical results.

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