A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations

T. Kinoshita, T. Kimura, M. T. Nakao

研究成果: Article査読

5 被引用数 (Scopus)

抄録

We present constructive a posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations (ODEs) on a bounded interval. Here, "constructive" indicates that we can obtain bounds of the operator norm in which all constants are explicitly given or are represented in a numerically computable form. In general, it is difficult to estimate these inverse operators a priori. We, therefore, propose a technique for obtaining a posteriori estimates by using Galerkin approximation of inverse operators. This type of estimation will play an important role in the numerical verification of solutions for initial value problems in nonlinear ODEs as well as for parabolic initial boundary value problems.

本文言語English
ページ(範囲)1622-1636
ページ数15
ジャーナルJournal of Computational and Applied Mathematics
236
6
DOI
出版ステータスPublished - 2011 10 15
外部発表はい

ASJC Scopus subject areas

  • 計算数学
  • 応用数学

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