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

4 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

Fingerprint

A Posteriori Estimates
Linear Ordinary Differential Equations
Initial value problems
Ordinary differential equations
Initial Value Problem
Mathematical operators
Operator
Boundary value problems
Numerical Verification
Operator Norm
Galerkin Approximation
Nonlinear Ordinary Differential Equations
Parabolic Problems
Initial-boundary-value Problem
Interval
Estimate

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations. / Kinoshita, T.; Kimura, T.; Nakao, M. T.

In: Journal of Computational and Applied Mathematics, Vol. 236, No. 6, 15.10.2011, p. 1622-1636.

Research output: Contribution to journalArticle

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