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

Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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
Volume38
Issue number1-3
DOIs
Publication statusPublished - 1991 Dec 23
Externally publishedYes

Fingerprint

Nonlinear Parabolic Problems
Parabolic Problems
Numerical Verification
Schauder Fixed Point Theorem
Existence of Weak Solutions
Finite Element Approximation
Initial-boundary-value Problem
Error Bounds
Boundary value problems
Error Estimates
Numerical methods
Approximate Solution
Exact Solution
Numerical Methods
Numerical Examples

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Solving nonlinear parabolic problems with result verification. Part I : one-space dimensional case. / Nakao, Mitsuhiro T.

In: Journal of Computational and Applied Mathematics, Vol. 38, No. 1-3, 23.12.1991, p. 323-334.

Research output: Contribution to journalArticle

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