Title: Sinc collocation method: solution of a class of strongly nonlinear two-point boundary value problems

Authors: M. Nabati; A. Barati; M. Jalalvand; J. Rashidinia

Addresses: Abadan Faculty of Petroleum, Department of Basic Sciences, Petroleum University of Technology, Abadan, 6318714331, Iran ' Islam-abad Faculty of Engineering, Razi University, Kermanshah, 6714414971, Iran ' Faculty of Mathematical Sciences and Computer, Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, 6135783151, Iran ' School of Mathematics, Iran University of Sciences and Technology, Tehran, 1684613114, Iran

Abstract: In this study, Sinc-collocation methods based on single and double exponential transformations for finding solution of a class of nonlinear second order two-point boundary value problems were developed, and their properties were enumerated. The presented methods are shown to reduce the solution of nonlinear two-point boundary value problems to the system of nonlinear algebraic equations. The convergence and error analysis of the method has been investigated, also the upper bound of the error has been calculated as exponential form. To show the efficiency, ability and high accuracy of the method, several examples have been considered. The obtained results of Sinc methods based on single and double exponential transformations were compared with each other, and also with those of the existing numerical results of methods reported in the literatures. The numerical results confirm that these methods rapidly converge and have a considerably efficient and accurate nature.

Keywords: Sinc function; collocation method; nonlinear problems of BVP; single and double exponential transformation.

DOI: 10.1504/IJCSM.2023.133516

International Journal of Computing Science and Mathematics, 2023 Vol.18 No.1, pp.1 - 16

Accepted: 23 Feb 2021
Published online: 19 Sep 2023 *

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