Abstract
A method for numerical solution of Volterra integral equations of the second kind with a weakly singular kernel based on the double exponential (DE) transformation is proposed. In this method we first express the approximate solution in the form of a Sinc expansion based on the double exponential transformation by Takahasi and Mori in 1974 followed by collocation at the Sinc points. We also apply the DE formula to the kernel integration. In every sample equation a numerical solution with very high accuracy is obtained and a nearly exponential convergence rate exp(−cM/logM),c > 0 in the error is observed whereM is a parameter representing the number of terms in the Sinc expansion. We compared the result with the one based on the single exponential (SE) transformation by Riley in 1992 which made us confirm the high efficiency of the present method.
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Partially supported by the Grant-in-Aid for the 21st Century COE Research by the Ministry of Education, Culture, Sports, Science and Technology, and also by the Grand-in-Aid for Scientific Research (C) by Japan Society for the Promotion of Sciences.
In pin yin: Aheniyazi Nuermaimaiti.
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Mori, M., Nurmuhammad, A. & Murai, T. Numerical solution of Volterra integral equations with weakly singular kernel based on the DE-sinc method. Japan J. Indust. Appl. Math. 25, 165 (2008). https://doi.org/10.1007/BF03167518
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DOI: https://doi.org/10.1007/BF03167518