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The sinc-Galerkin method and its applications on singular Dirichlet-type boundary value problems

Aydin Secer1* and Muhammet Kurulay2

Author Affiliations

1 Department of Mathematical Engineering, Faculty of Chemical and Metallurgical Engineering, Yildiz Technical University, Davutpasa, İstanbul, 34210, Turkey

2 Department of Mathematics, Faculty of Art and Sciences, Yildiz Technical University, Davutpasa, İstanbul, 34210, Turkey

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Boundary Value Problems 2012, 2012:126  doi:10.1186/1687-2770-2012-126

Published: 29 October 2012


The application of the sinc-Galerkin method to an approximate solution of second-order singular Dirichlet-type boundary value problems were discussed in this study. The method is based on approximating functions and their derivatives by using the Whittaker cardinal function. The differential equation is reduced to a system of algebraic equations via new accurate explicit approximations of the inner products without any numerical integration which is needed to solve matrix system. This study shows that the sinc-Galerkin method is a very effective and powerful tool in solving such problems numerically. At the end of the paper, the method was tested on several examples with second-order Dirichlet-type boundary value problems.

sinc-Galerkin method; sinc basis functions; Dirichlet-type boundary value problems; LU decomposition method