Improvement of a sinc-collocation method for Fredholm integral equations of the second kind
The main purpose of this paper is to improve the Rashidinia-Zarebnia scheme (RZ Scheme) proposed in [\textit{J. Rashidinia} and \textit{M. Zarebnia}, Appl. Math. Comput. 168, No. 2, 806--822 (2005; Zbl 1082.65601)]. Two alternative schemes are proposed. The first scheme is obtained by modifying the RZ scheme so that it becomes more practical, and natural from 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.
scientific article; zbMATH DE number 5935009
scientific article