Backward error analysis of a full discretization scheme for a class of semilinear parabolic partial differential equations

Research output: Contribution to journalArticle

  • 3 Citations

Abstract

A numerical method for reaction–diffusion equations with analytic nonlinearity is presented, for which a rigorous backward error analysis is possible. We construct a modified equation, which describes the behavior of the full discretization scheme up to exponentially small errors in the step size. In the construction the numerical scheme is first exactly embedded into a nonautonomous equation. This equation is then averaged with only exponentially small remainder terms. The long-time behavior near hyperbolic equilibria, the persistence of homoclinic orbits and regularity properties are analyzed.
LanguageEnglish
Pages805-826
JournalNonlinear Analysis: Theory Methods & Applications
Volume52
Issue number3
DOIs
StatusPublished - Feb 2003

Fingerprint

Backward Error Analysis
Nonautonomous Equation
Discretization Scheme
Regularity Properties
Homoclinic Orbit
Parabolic Partial Differential Equations
Modified Equations
Long-time Behavior
Error term
Reaction-diffusion Equations
Semilinear
Persistence
Error analysis
Numerical Scheme
Partial differential equations
Numerical methods
Orbits
Numerical Methods
Nonlinearity
Class

Cite this

@article{76cd9c60413a4ce4b113ea81307c0c9a,
title = "Backward error analysis of a full discretization scheme for a class of semilinear parabolic partial differential equations",
abstract = "A numerical method for reaction–diffusion equations with analytic nonlinearity is presented, for which a rigorous backward error analysis is possible. We construct a modified equation, which describes the behavior of the full discretization scheme up to exponentially small errors in the step size. In the construction the numerical scheme is first exactly embedded into a nonautonomous equation. This equation is then averaged with only exponentially small remainder terms. The long-time behavior near hyperbolic equilibria, the persistence of homoclinic orbits and regularity properties are analyzed.",
author = "Karsten Matthies",
year = "2003",
month = "2",
doi = "10.1016/S0362-546X(02)00134-7",
language = "English",
volume = "52",
pages = "805--826",
journal = "Nonlinear Analysis: Theory Methods & Applications",
issn = "0362-546X",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - Backward error analysis of a full discretization scheme for a class of semilinear parabolic partial differential equations

AU - Matthies,Karsten

PY - 2003/2

Y1 - 2003/2

N2 - A numerical method for reaction–diffusion equations with analytic nonlinearity is presented, for which a rigorous backward error analysis is possible. We construct a modified equation, which describes the behavior of the full discretization scheme up to exponentially small errors in the step size. In the construction the numerical scheme is first exactly embedded into a nonautonomous equation. This equation is then averaged with only exponentially small remainder terms. The long-time behavior near hyperbolic equilibria, the persistence of homoclinic orbits and regularity properties are analyzed.

AB - A numerical method for reaction–diffusion equations with analytic nonlinearity is presented, for which a rigorous backward error analysis is possible. We construct a modified equation, which describes the behavior of the full discretization scheme up to exponentially small errors in the step size. In the construction the numerical scheme is first exactly embedded into a nonautonomous equation. This equation is then averaged with only exponentially small remainder terms. The long-time behavior near hyperbolic equilibria, the persistence of homoclinic orbits and regularity properties are analyzed.

UR - http://dx.doi.org/10.1016/S0362-546X(02)00134-7

U2 - 10.1016/S0362-546X(02)00134-7

DO - 10.1016/S0362-546X(02)00134-7

M3 - Article

VL - 52

SP - 805

EP - 826

JO - Nonlinear Analysis: Theory Methods & Applications

T2 - Nonlinear Analysis: Theory Methods & Applications

JF - Nonlinear Analysis: Theory Methods & Applications

SN - 0362-546X

IS - 3

ER -