Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
special section
Numerical existence theorem for solutions of two-point boundary value problems of nonlinear differential equations
Akitoshi TakayasuShin'ichi OishiTakayuki Kubo
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2010 Volume 1 Issue 1 Pages 105-118

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Abstract

In this paper, a numerical method is presented for verifying the existence and uniqueness of solutions to two-point boundary value problems of nonlinear ordinary differential equations. Taking into account every error of numerical computations such as the discretization error and the rounding error, this method also provides mathematically guaranteed error bounds between approximations obtained by numerical computations and the exact solution whose existence is proven by the numerical existence theorem, which is based on the Newton-Kantorovich theorem. Finally, illustrative numerical results are presented for showing the usefulness of the method.

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© 2010 The Institute of Electronics, Information and Communication Engineers
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