Presentation 1998/3/13
A Numerical Method of Proving Existence of Solutions for Nonlinear Ordinary Differential Equations Using Interval Newton Mappings
Takao SOMA, Shin'ichi OISHI, Kazuo HORIUCHI,
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Abstract(in English) In this report, a method is presented to prove existence of exact solutions of nonlinear boundary value problems of ordinary differential equations. Concretely, we define infinite dimensional extension of Interval Newton mapping and show that it is possible to compute the image of Interval Newton mapping numerically. It is also possible to obtain sharp error estimation of approximate solutions. Taking an example, the result of validation are also presented.
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Keyword(in English) Numerical Computation with Guaranteed Accuracy / Interval Newton Mapping / Ordinary Differential Equations / Interval Analysis
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Committee NLP
Conference Date 1998/3/13(1days)
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Registration To Nonlinear Problems (NLP)
Language JPN
Title (in Japanese) (See Japanese page)
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Title (in English) A Numerical Method of Proving Existence of Solutions for Nonlinear Ordinary Differential Equations Using Interval Newton Mappings
Sub Title (in English)
Keyword(1) Numerical Computation with Guaranteed Accuracy
Keyword(2) Interval Newton Mapping
Keyword(3) Ordinary Differential Equations
Keyword(4) Interval Analysis
1st Author's Name Takao SOMA
1st Author's Affiliation School of Science and Engineering, Waseda University()
2nd Author's Name Shin'ichi OISHI
2nd Author's Affiliation School of Science and Engineering, Waseda University
3rd Author's Name Kazuo HORIUCHI
3rd Author's Affiliation School of Science and Engineering, Waseda University
Date 1998/3/13
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Volume (vol) vol.97
Number (no) 592
Page pp.pp.-
#Pages 6
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