Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations - Collections

＜technical report＞
Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations

Creator	Creator Name Minamoto, Teruya 皆本, 晃弥 Affiliation Affiliation Name Department of Informatics Kyushu University 九州大学大学院システム情報科学研究院情報理学部門
Language	English
Publisher	Department of Informatics, Kyushu University
Publisher	九州大学大学院システム情報科学研究院情報理学部門
Date	1999-04-06
Source Title	DOI Technical Report
Vol	160
Publication Type	Accepted Manuscript
Access Rights	open access
Related DOI	DOI Technical Report \|\| 160
Related DOI	http://www.i.kyushu-u.ac.jp/research/report.html
Related URI	DOI Technical Report \|\| 160
Related URI	http://www.i.kyushu-u.ac.jp/research/report.html
Relation	DOI Technical Report \|\| 160
Relation	http://www.i.kyushu-u.ac.jp/research/report.html
Abstract	We consider a numerical method to verify the existence and uniqueness of the solutions of nonlinear hyperbolic problems with guaranteed error bounds. Using a $ C^1 $ finite element solution and an ine...quality constituting a bound on the norm of the inverse operator of the linearized operator, we numerically construct a set of functions which satisfy the hypothesis of Banach's fixed point theorem for a continuous map on $ L^p $ -space in a computer. We present detailed verification procedures and give some numerical examples.show more

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