Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case

Teruya Minamoto, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, we describe a numerical method to verify the solutions with guaranteed error bounds for nonlinear parabolic problems in one dimensional case. It is based on Plum's method for formulating the problem and weak formulation for estimating explicitly the inverse norm of the linearized operator. We introduce some weighted norms on time-dependent Sobolev spaces, which play an important role in the application of our method. We present detailed verification procedures by using this weighted norm and show some numerical examples.

Original languageEnglish
Pages (from-to)137-147
Number of pages11
JournalReliable Computing
Volume3
Issue number2
Publication statusPublished - 1997
Externally publishedYes

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Numerical Verification
Sobolev spaces
Weighted Norm
Nonlinear Parabolic Equations
Numerical methods
Nonlinear Parabolic Problems
Weak Formulation
Sobolev Spaces
Error Bounds
Numerical Methods
Verify
Norm
Numerical Examples
Operator

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics

Cite this

Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case. / Minamoto, Teruya; Nakao, Mitsuhiro T.

In: Reliable Computing, Vol. 3, No. 2, 1997, p. 137-147.

Research output: Contribution to journalArticle

Minamoto, Teruya ; Nakao, Mitsuhiro T. / Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case. In: Reliable Computing. 1997 ; Vol. 3, No. 2. pp. 137-147.
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