Convergence Analysis of Legendre-Collocation Spectral Methods for Second Order Volterra Integro-Differential Equation with Delay
Year: 2019
Author: Weishan Zheng, Yanping Chen, Yunqing Huang
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 486–500
Abstract
In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with delay. We provide a rigorous error analysis for the proposed method. The spectral rate of convergence for the proposed method is established in both $L^{2}$-norm and $L^{\infty}$-norm. In the end, the numerical experiment is illustrated to confirm the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0121
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 486–500
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Convergence analysis Legendre-spectral method second order Volterra integro-differential equation delay error analysis.