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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2013; 50(4): 715-725

Printed July 1, 2013

https://doi.org/10.4134/JKMS.2013.50.4.715

Copyright © The Korean Mathematical Society.

Numerical method for a 2nth-order boundary value problem

Chenmei Xu, Shuai Jian, and Bo Wang

Henan University, Chinese Academy of Sciences, Henan University

Abstract

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In this paper, a finite difference scheme for a two-point boun\-dary value problem of 2nth-order ordinary differential equations is presented. The convergence and uniqueness of the solution for the scheme are proved by means of theories on matrix eigenvalues and norm. Numerical examples show that our method is very simple and effective, and that this method can be used effectively for other types of boundary value problems.

Keywords: boundary valve problem, finite difference scheme, 2nth-order ordinary differential equation, total truncation error

MSC numbers: 65L10, 65L70

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