Numerical verification methods for solutions of ordinary and partial differential equations

M. T. Nakao

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

In this article, we describe on a state of the art of validated numerical computations for solutions of differential equations. A brief overview of the main techniques for self-validating numerics for initial and boundary value problems in ordinary and partial differential equations including eigenvalue problems will be presented. A fairly detailed introductions are given for the author's own method related to second-order elliptic boundary for the author's own method related to second-order elliptic boundary value problems. Many references which seem to be useful for readers are supplied at the end of the article.

Original languageEnglish
Pages (from-to)321-356
Number of pages36
JournalNumerical Functional Analysis and Optimization
Volume22
Issue number3-4
DOIs
Publication statusPublished - 2001 May
Externally publishedYes

Fingerprint

Numerical Verification
Ordinary differential equations
Boundary value problems
Partial differential equations
Ordinary differential equation
Partial differential equation
Initial value problems
Elliptic Boundary Value Problems
Numerics
Numerical Computation
Eigenvalue Problem
Initial Value Problem
Differential equations
Boundary Value Problem
Differential equation

Keywords

  • Computer assisted proof in analysis
  • Nonlinear differential equation
  • Numerical verification

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

Cite this

Numerical verification methods for solutions of ordinary and partial differential equations. / Nakao, M. T.

In: Numerical Functional Analysis and Optimization, Vol. 22, No. 3-4, 05.2001, p. 321-356.

Research output: Contribution to journalArticle

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