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Convergence analysis of the spectral methods for weakly singular Volterra integro-differential equations with smooth solutions. (English) Zbl 1262.45005
Summary: The theory of a class of spectral methods is extended to Volterra integrodifferential equations which contain a weakly singular kernel (t-s) -μ with 0<μ<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.
MSC:
45J05Integro-ordinary differential equations
65R20Integral equations (numerical methods)