Improvement of a sinc-collocation method for Fredholm integral equations of the second kind
type: Item
instance of: scholarly article
title: Improvement of a sinc-collocation method for Fredholm integral equations of the second kind
zbMATH Open document ID: 1221.65341
author: Tomoaki Okayama
author: Takayasu Matsuo
author: Masaaki Sugihara
published in: BIT
publication date: 2011-08-02T00:00:00Z
review text: 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.
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 5935009
zbMATH Keywords: sinc-collocation method
zbMATH Keywords: Frehdolm integral equation
zbMATH Keywords: Variable transformation
MaRDI profile type: Publication
full work available at URL: s10543-010-0289-x
OpenAlex ID: W1980170244
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DOI: 10.1007/S10543-010-0289-X
description: scientific article; zbMATH DE number 5935009