Numerical solution of integral equations by means of the Sinc collocation method based on the double exponential transformation

Authors:
Mayinur Muhammad;Ahniyaz Nurmuhammad;Masatake Mori;Masaaki Sugihara
Affiliations:
Department of Mathematical Sciences, Tokyo Denki University, Hatoyama-cho, Hiki-gun, Saitama 350-0394, Japan;Department of Mathematical Sciences, Tokyo Denki University, Hatoyama-cho, Hiki-gun, Saitama 350-0394, Japan;Department of Mathematical Sciences, Tokyo Denki University, Hatoyama-cho, Hiki-gun, Saitama 350-0394, Japan;Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya, 464-8603, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 5
Cited 2

Computational methods for integral equations

Computational methods for integral equations
The double-exponential transformation in numerical analysis

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Computer Methods for Mathematical Computations

Computer Methods for Mathematical Computations
Hypersingular kernel integration in 3D Galerkin boundary element method

Journal of Computational and Applied Mathematics
Double exponential formulas for numerical indefinite integration

Journal of Computational and Applied Mathematics

Imposing boundary conditions in Sinc method using highest derivative approximation

Journal of Computational and Applied Mathematics
De-Sinc numerical methods

Proceedings of the 2009 conference on Symbolic numeric computation

Quantified Score

Hi-index	7.29

Visualization

Abstract

Numerical solution of linear integral equations by means of the Sinc collocation method based on the double exponential transformation, abbreviated the DE transformation, is considered. We first apply the method to the Volterra integral equation of the second kind and then to the Volterra equation of the first kind. This method is also applied to the Fredholm integral equation of the second kind. For the Volterra equations we employed a formula for numerical indefinite integration developed by Muhammad and Mori obtained by applying the DE transformation incorporated into the Sinc expansion of the integrand, while for the Fredholm equation we employed the conventional DE transformation for definite integrals. An error analysis of the method is given and in every case a convergence rate of O(exp(-cN/log N)) for the error is established where N is a parameter representing the number of terms of the Sinc expansion. Also, the condition of the matrix of the main system of linear equations is watched through an estimate of the condition number returned by the program. Numerical examples show the convergence rate mentioned above and confirm the high efficiency of the present method.