Double exponential transformation in the Sinc-collocation method for a boundary value problem with fourth-order ordinary differential equation

Authors:
Ahniyaz Nurmuhammad;Mayinur Muhammad;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

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Abstract

In this paper we consider a Sinc-collocation method for the two-point boundary value problem of fourth-order ordinary differential equation incorporated with the double exponential transformation (abbreviated as the DE transformation). By this method a convergence rate O(exp(-cN/logN)) where N is a parameter representing the number of terms in the Sinc approximation is attained. We compared the result with ones based on the single exponential transformation which made us confirm the high efficiency of the present method.