Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels |
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Authors: | Shuhuang Xiang Hermann Brunner |
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Institution: | 1. Department of Applied Mathematics and Software, Central South University, Changsha, Hunan, 410083, P.R. China 2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada 3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
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Abstract: | In this paper, we introduce efficient methods for the approximation of solutions to weakly singular Volterra integral equations of the second kind with highly oscillatory Bessel kernels. Based on the asymptotic analysis of the solution, we derive corresponding convergence rates in terms of the frequency for the Filon method, and for piecewise constant and linear collocation methods. We also present asymptotic schemes for large values of the frequency. These schemes possess the property that the numerical solutions become more accurate as the frequency increases. |
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