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

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

Published online: 2018-05

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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.

• Keywords

Volterra integro-differential equations, spectral Jacobi-collocation method, pantograph delay, weakly singular kernel.

65R20, 65M70, 45D05

• BibTex
• RIS
• TXT
@Article{AAMM-8-648, author = {Xiulian Shi , and Chen , Yanping}, title = {Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {4}, pages = {648--669}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1088}, url = {http://global-sci.org/intro/article_detail/aamm/12108.html} }
TY - JOUR T1 - Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels AU - Xiulian Shi , AU - Chen , Yanping JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 648 EP - 669 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2015.m1088 UR - https://global-sci.org/intro/article_detail/aamm/12108.html KW - Volterra integro-differential equations, spectral Jacobi-collocation method, pantograph delay, weakly singular kernel. AB -

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.

Xiulian Shi & Yanping Chen. (2020). Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels. Advances in Applied Mathematics and Mechanics. 8 (4). 648-669. doi:10.4208/aamm.2015.m1088
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