Spectral Collocation Methods for Second-Order Volterra Integro-Differential Equations with Weakly Singular Kernels
Year: 2020
Author: Xiulian Shi, Yanping Chen, Yunqing Huang, Fenglin Huang
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 480–502
Abstract
In this paper, a Jacobi spectral collocation approximation is proposed for the solution of second-order Volterra integro-differential equations with weakly singular kernels. The solution of such equations usually exhibits a singular behaviour at the origin. By using some suitable variable transformations, we obtain a new equation which is still weakly singular, but whose solution is as smooth as we like. Then the resulting equation is solved by standard spectral methods. We establish a rigorous error analysis for the proposed method, which shows that the numerical errors decay exponentially in L∞-norm and weighted L2-norm. Finally, to perform the numerical simulation, a test example is considered with non-smooth solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0056
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 480–502
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Volterra integro-differential equations weakly singular kernel spectral collocation methods.
Author Details
Xiulian Shi Email
Yanping Chen Email
Yunqing Huang Email
Fenglin Huang Email
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