Solving nonlinear parabolic problems with result verification. Part I: one-space dimensional case

Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

11 Citations (Scopus)


We propose some numerical methods for the automatic proof of existence of weak solutions for parabolic initial boundary value problems with one space dimension. It also means that one can obtain a posteriori error bounds for the approximate solutions of the problems. Based upon Schauder's fixed-point theorem, a verification condition is formulated and, by the use of finite-element approximation and its error estimates for a simple parabolic problem, we present a numerical verification algorithm of exact solutions in a computer. Some numerical examples which are verified by the method are illustrated.

Original languageEnglish
Pages (from-to)323-334
Number of pages12
JournalJournal of Computational and Applied Mathematics
Issue number1-3
Publication statusPublished - 1991 Dec 23
Externally publishedYes



  • error estimates
  • finite-element method
  • fixed-point theorem
  • Parabolic problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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