Volume 8, Issue 4
Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels

Xiulian Shi and Yanping Chen

10.4208/aamm.2015.m1088

Adv. Appl. Math. Mech., 8 (2016), pp. 648-669.

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  • Abstract

A spectral Jacobi-collocation approximation is proposed for Volterra delay integro-differential equations with weakly singular kernels. In this paper, we consider the special case that the underlying solutions of equations are sufficiently smooth. We provide a rigorous error analysis for the proposed method, which shows that both the errors of approximate solutions and the errors of approximate derivatives decay exponentially in L ∞ norm and weighted L 2 norm. Finally, two numerical examples are presented to demonstrate our error analysis.

  • History

Published online: 2018-05

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