文章基本信息

标题：The coupled method for singularly perturbed Volterra integro-differential equations
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作者：Xia Tao ; Yinghui Zhang
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-16
DOI：10.1186/s13662-019-2139-8
出版社：Hindawi Publishing Corporation
摘要：In this work a coupled (LDG-CFEM) method for singularly perturbed Volterra integro-differential equations with a smooth kernel is implemented. The existence and uniqueness of the coupled solution is given, provided that the source function and the kernel function are sufficiently smooth. Furthermore, the coupled solution achieves the optimal convergence rate p + 1 in the L2 norm and a superconvergence rate 2p at nodes for the numerical solution Uˆ N with the one-sided flux inside the boundary layer region under layer-adapted meshes uniformly with respect to the singular perturbation parameter ϵ.
关键词：Singularly perturbed Volterra integro-differential equations ; The coupled (LDG-CFEM) method ; Layer-adapted meshes ; Uniform superconvergence