On the convergence rates of Filon methods for the solution of a Volterra integral equation with a highly oscillatory Bessel kernel |
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| Authors: | Junjie Ma Shuhuang Xiang Hongchao Kang |
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| Institution: | 1. School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, PR China;2. School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, PR China |
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| Abstract: | In this paper, based on the asymptotic property of the solution, we derive the corresponding convergence rates in terms of the frequency for the direct-Filon and linear continuous collocation methods, which solves an open problem in Brunner (2010) 1]. Numerical tests verify that the asymptotic orders obtained are optimal. |
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