Numerical blow-up of semilinear parabolic PDEs on unbounded domains in R2

Jiwei Zhang; Houde Han; Hermann BRUNNER

doi:10.1007/s10915-011-9467-5

Numerical blow-up of semilinear parabolic PDEs on unbounded domains in R²

Jiwei Zhang, Houde Han, Hermann BRUNNER^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

21 Citations (Scopus)

Abstract

We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains ω in R² whose solutions blow up in finite time. Of particular interest are the cases where ω = R² or ω is a sectorial domain in R². We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple adaptive time-stepping scheme to compute the solution of the resulting system of semilinear ODEs. The theoretical results are illustrated by a broad range of numerical examples.

Original language	English
Pages (from-to)	367-382
Number of pages	16
Journal	Journal of Scientific Computing
Volume	49
Issue number	3
DOIs	https://doi.org/10.1007/s10915-011-9467-5
Publication status	Published - Dec 2011

Scopus Subject Areas

Software
Theoretical Computer Science
Numerical Analysis
Engineering(all)
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Adaptive time-stepping
Finite difference spatial discretization
Finite-time blow-up
Local nonlinear boundary conditions
Sectorial domains
Semilinear PDEs
Unbounded spatial domains

Access to Document

10.1007/s10915-011-9467-5

Cite this

@article{b99ca1734a3a43088f6d85c0b5e84488,

title = "Numerical blow-up of semilinear parabolic PDEs on unbounded domains in R2",

abstract = "We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains ω in R2 whose solutions blow up in finite time. Of particular interest are the cases where ω = R2 or ω is a sectorial domain in R2. We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple adaptive time-stepping scheme to compute the solution of the resulting system of semilinear ODEs. The theoretical results are illustrated by a broad range of numerical examples.",

keywords = "Adaptive time-stepping, Finite difference spatial discretization, Finite-time blow-up, Local nonlinear boundary conditions, Sectorial domains, Semilinear PDEs, Unbounded spatial domains",

author = "Jiwei Zhang and Houde Han and Hermann BRUNNER",

note = "Funding Information: Acknowledgements The first author (J. Zhang) was supported in part by RGC and FRG of Hong Kong Baptist University. The research of the second author (H. Han) was supported by the NSFC Project No. 10971116. The work of the third author (H. Brunner) was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada and by the Hong Kong Research Grants Council (RGC).",

year = "2011",

month = dec,

doi = "10.1007/s10915-011-9467-5",

language = "English",

volume = "49",

pages = "367--382",

journal = "Journal of Scientific Computing",

issn = "0885-7474",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Numerical blow-up of semilinear parabolic PDEs on unbounded domains in R2

AU - Zhang, Jiwei

AU - Han, Houde

AU - BRUNNER, Hermann

N1 - Funding Information: Acknowledgements The first author (J. Zhang) was supported in part by RGC and FRG of Hong Kong Baptist University. The research of the second author (H. Han) was supported by the NSFC Project No. 10971116. The work of the third author (H. Brunner) was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada and by the Hong Kong Research Grants Council (RGC).

PY - 2011/12

Y1 - 2011/12

N2 - We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains ω in R2 whose solutions blow up in finite time. Of particular interest are the cases where ω = R2 or ω is a sectorial domain in R2. We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple adaptive time-stepping scheme to compute the solution of the resulting system of semilinear ODEs. The theoretical results are illustrated by a broad range of numerical examples.

AB - We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains ω in R2 whose solutions blow up in finite time. Of particular interest are the cases where ω = R2 or ω is a sectorial domain in R2. We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple adaptive time-stepping scheme to compute the solution of the resulting system of semilinear ODEs. The theoretical results are illustrated by a broad range of numerical examples.

KW - Adaptive time-stepping

KW - Finite difference spatial discretization

KW - Finite-time blow-up

KW - Local nonlinear boundary conditions

KW - Sectorial domains

KW - Semilinear PDEs

KW - Unbounded spatial domains

UR - http://www.scopus.com/inward/record.url?scp=84855197378&partnerID=8YFLogxK

U2 - 10.1007/s10915-011-9467-5

DO - 10.1007/s10915-011-9467-5

M3 - Journal article

AN - SCOPUS:84855197378

SN - 0885-7474

VL - 49

SP - 367

EP - 382

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 3

ER -