A computer-assisted proof of the existence of solutions to a boundary value problem with an integral boundary condition

Oswald Fogelklou, Warwick Tucker, Gunilla Kreiss, Malin Siklosi

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4 Citations (Scopus)

Abstract

In this paper, we present a computer-assisted method that establishes the existence and local uniqueness of a stationary solution to the viscous Burgers' equation. The problem formulation involves a left boundary condition and one integral boundary condition, which is a variation of a previous approach.

Original languageEnglish
Pages (from-to)1227-1243
Number of pages17
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume16
Issue number3
DOIs
Publication statusPublished - 1 Mar 2011
Externally publishedYes

Keywords

  • Computer-assisted proof
  • Enclosure
  • Existence
  • Fixed-point problems
  • Numerical verification
  • Two-point boundary value problems
  • Viscous Burgers' equation

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