Abstract
A Sinc-collocation scheme for Fredholm integral equations of the second kind was proposed by Rashidinia–Zarebnia in 2005. In this paper, two improved versions of the Sinc-collocation scheme are presented. The first version is obtained by improving the scheme so that it becomes more practical, and natural from a theoretical view point. Then it is rigorously proved that the convergence rate of the modified scheme is exponential, as suggested in the literature. In the second version, the variable transformation employed in the original scheme, the “tanh transformation”, is replaced with the “double exponential transformation”. It is proved that the replacement improves the convergence rate drastically. Numerical examples which support the theoretical results are also given.
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Communicated by Lothar Reichel.
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Okayama, T., Matsuo, T. & Sugihara, M. Improvement of a Sinc-collocation method for Fredholm integral equations of the second kind. Bit Numer Math 51, 339–366 (2011). https://doi.org/10.1007/s10543-010-0289-x
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DOI: https://doi.org/10.1007/s10543-010-0289-x