Improvement of a Sinc-collocation method for Fredholm integral equations of the second kind
- 154 Downloads
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.
KeywordsSinc-collocation method Fredholm integral equation Variable transformation
Mathematics Subject Classification (2000)65R20
Unable to display preview. Download preview PDF.
- 4.Golberg, M.A., Chen, C.S.: Discrete Projection Methods for Integral Equations. Computational Mechanics, Southampton (1996) Google Scholar
- 10.Okayama, T., Matsuo, T., Sugihara, M.: Error estimates with explicit constants for Sinc approximation, Sinc quadrature and Sinc indefinite integration. Mathematical Engineering Technical Reports 2009-01, The University of Tokyo (2009) Google Scholar