Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions
نویسندگان
چکیده
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 L2-norm. The numerical examples are given to illustrate the theoretical results. AMS subject classifications: 45J05, 65R20
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