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

doi:10.1016/j.cnsns.2010.07.008

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

Research output: Contribution to journal › Article › Research › peer-review

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 language	English
Pages (from-to)	1227-1243
Number of pages	17
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	16
Issue number	3
DOIs	https://doi.org/10.1016/j.cnsns.2010.07.008
Publication status	Published - 1 Mar 2011
Externally published	Yes

Keywords

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

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10.1016/j.cnsns.2010.07.008

Cite this

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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.",

keywords = "Computer-assisted proof, Enclosure, Existence, Fixed-point problems, Numerical verification, Two-point boundary value problems, Viscous Burgers' equation",

author = "Oswald Fogelklou and Warwick Tucker and Gunilla Kreiss and Malin Siklosi",

year = "2011",

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A computer-assisted proof of the existence of solutions to a boundary value problem with an integral boundary condition. / Fogelklou, Oswald; Tucker, Warwick; Kreiss, Gunilla et al.
In: Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 3, 01.03.2011, p. 1227-1243.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - A computer-assisted proof of the existence of solutions to a boundary value problem with an integral boundary condition

AU - Fogelklou, Oswald

AU - Tucker, Warwick

AU - Kreiss, Gunilla

AU - Siklosi, Malin

PY - 2011/3/1

Y1 - 2011/3/1

N2 - 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.

AB - 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.

KW - Computer-assisted proof

KW - Enclosure

KW - Existence

KW - Fixed-point problems

KW - Numerical verification

KW - Two-point boundary value problems

KW - Viscous Burgers' equation

UR - https://www.scopus.com/pages/publications/77957361825

U2 - 10.1016/j.cnsns.2010.07.008

DO - 10.1016/j.cnsns.2010.07.008

M3 - Article

AN - SCOPUS:77957361825

SN - 1007-5704

VL - 16

SP - 1227

EP - 1243

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 3

ER -

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

Abstract

Keywords

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