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

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

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1622-1636
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume236
Issue number6
DOIs
Publication statusPublished - 2011 Oct 15
Externally publishedYes

Keywords

  • Constructive a posteriori estimates
  • Finite element method
  • Linear ODEs

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations'. Together they form a unique fingerprint.

  • Cite this