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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The authors are grateful to the two anonymous referees for their useful comments and constructive suggestions for improvement of this paper.
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Communicated by Anne Kværnø.
This work is supported partly by NSF of China (No.11071260).
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Xiang, S., Brunner, H. Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels. Bit Numer Math 53, 241–263 (2013). https://doi.org/10.1007/s10543-012-0399-8
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DOI: https://doi.org/10.1007/s10543-012-0399-8