Abstract
This paper focuses on the numerical solution for Volterra integral equations of the first kind with highly oscillatory Bessel kernel and highly oscillatory triangle function on the right-hand side. We first establish a new existence theorem of solutions for such equations, and then, the explicit formulas of the solution are derived based on Laplace and inverse Laplace transforms. Furthermore, high-order accurate numerical solutions for approximating the explicit solution are further deduced by applying the Clenshaw–Curtis–Filon method and other effective numerical methods. Preliminary numerical results not only show the exact formulas of the solution, but also present the accuracy of the approximations.
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Funding
This work is supported partly by NSF of China (Nos. 11371376, 11771454), the Innovation-Driven Project, the Mathematics and Interdisciplinary Sciences Project of Central South University and the Fundamental Research Funds for the Central Universities of Central South University (No. 2017zzts060), the Natural Science Foundation of Hunan Province (No. 2017JJ3092), and scientific research project of Department of Education of Hunan Province (No. 17C0677).
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Li, B., Xiang, S. & Liu, G. Laplace transforms for evaluation of Volterra integral equation of the first kind with highly oscillatory kernel. Comp. Appl. Math. 38, 116 (2019). https://doi.org/10.1007/s40314-019-0892-7
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DOI: https://doi.org/10.1007/s40314-019-0892-7