Numerical Method for Singularly Perturbed Parabolic Equations in Unbounded Domains in the Case of Solutions Growing at Infinity
Abstract: An initial-boundary value problem is considered in an unbounded do- main on the x-axis for a singularly perturbed parabolic reaction-diffusion equation. For small values of the parameter ε, a parabolic boundary layer arises in a neighbourhood of the lateral part of the boundary. In this problem, the error of a discrete solution in the maximum norm grows without bound even for fixed values of the parameter ε. In the present paper, the proximity of solutions of the initial-boundary value problem and of its numerical approximations is considered. Using the method of special grids condensing in a neighbourhood of the boundary layer, a special finite difference scheme converging ε-uniformly in the weight maximum norm has been constructed.
- Standort
-
Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
-
Online-Ressource
- Sprache
-
Englisch
- Erschienen in
-
Numerical Method for Singularly Perturbed Parabolic Equations in Unbounded Domains in the Case of Solutions Growing at Infinity ; volume:9 ; number:1 ; year:2009 ; pages:100-110
Computational methods in applied mathematics ; 9, Heft 1 (2009), 100-110
- Urheber
-
Shishkin, G. I.
- DOI
-
10.2478/cmam-2009-0006
- URN
-
urn:nbn:de:101:1-2410261621328.708257451613
- Rechteinformation
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
-
15.08.2025, 07:31 MESZ
Datenpartner
Dieses Objekt wird bereitgestellt von:
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Shishkin, G. I.
Ähnliche Objekte (12)
Long term behaviour of singularly perturbed parabolic degenerated equation
Accurate numerical scheme for singularly perturbed parabolic delay differential equation
Approximation of Singularly Perturbed Parabolic Reaction-Diffusion Equations with Nonsmooth Data
Singularly perturbed differential equations
Singularly perturbed boundary value problems
Singularly Perturbed Oscillators with Exponential Nonlinearities
An efficient numerical approach for singularly perturbed time delayed parabolic problems with two-parameters
Fitted mesh scheme for singularly perturbed parabolic convection–diffusion problem exhibiting twin boundary layers
Gaussian quadrature method with exponential fitting factor for two-parameter singularly perturbed parabolic problem
Numerical algorithms based on splines for singularly perturbed parabolic partial differential equations with mixed shifts
A diagonal preconditioner for singularly perturbed problems
Cellular diffusion processes in singularly perturbed domains
Long term behaviour of singularly perturbed parabolic degenerated equation
Accurate numerical scheme for singularly perturbed parabolic delay differential equation
Approximation of Singularly Perturbed Parabolic Reaction-Diffusion Equations with Nonsmooth Data
Singularly perturbed differential equations
Singularly perturbed boundary value problems
Singularly Perturbed Oscillators with Exponential Nonlinearities
An efficient numerical approach for singularly perturbed time delayed parabolic problems with two-parameters
Fitted mesh scheme for singularly perturbed parabolic convection–diffusion problem exhibiting twin boundary layers
Gaussian quadrature method with exponential fitting factor for two-parameter singularly perturbed parabolic problem
Numerical algorithms based on splines for singularly perturbed parabolic partial differential equations with mixed shifts
A diagonal preconditioner for singularly perturbed problems
Cellular diffusion processes in singularly perturbed domains
Long term behaviour of singularly perturbed parabolic degenerated equation
Accurate numerical scheme for singularly perturbed parabolic delay differential equation
Approximation of Singularly Perturbed Parabolic Reaction-Diffusion Equations with Nonsmooth Data
Singularly perturbed differential equations
Singularly perturbed boundary value problems
Singularly Perturbed Oscillators with Exponential Nonlinearities
An efficient numerical approach for singularly perturbed time delayed parabolic problems with two-parameters
Fitted mesh scheme for singularly perturbed parabolic convection–diffusion problem exhibiting twin boundary layers
Gaussian quadrature method with exponential fitting factor for two-parameter singularly perturbed parabolic problem
Numerical algorithms based on splines for singularly perturbed parabolic partial differential equations with mixed shifts
A diagonal preconditioner for singularly perturbed problems