Numerical verification methods for solutions of ordinary and partial differential equations

M. T. Nakao

Research output: Contribution to journalArticle

52 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

Keywords

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

ASJC Scopus subject areas

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

Fingerprint Dive into the research topics of 'Numerical verification methods for solutions of ordinary and partial differential equations'. Together they form a unique fingerprint.

  • Cite this