On the implementation of discontinuous Galerkin methods for Volterra integral equations with highly oscillatory Bessel kernels

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• 作者：Shuhuang Xiang ; ^{xiangsh@mail.csu.edu.cn} ; Kaixian He
• 关键词：Discontinuous Galerkin method ; Bessel function ; High oscillation ; Volterra integral equation ; Weak singularity
• 刊名：Applied Mathematics and Computation
• 出版年：2013
• 出版时间：1 January, 2013
• 年：2013
• 卷：219
• 期：9
• 页码：4884-4891
• 全文大小：193 K

文摘

In this paper, we consider implementation of discontinuous Galerkin methods for (weakly singular) Volterra integral equations of first and second kinds with highly oscillatory Bessel kernels, which cost the same operations independent of large values of frequencies. Preliminary numerical results show that the proposed method is efficient for verifying accuracy of approximate solutions.