Complete flux scheme for elliptic singularly perturbed differential–difference equations

Sunil Kumar (Corresponding author), B.V. Rathish Kumar, J.H.M. ten Thije Boonkkamp

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In this study, we propose a new scheme named as complete flux scheme (CF-scheme) based on the finite volume method for solving singularly perturbed differential–difference equations (SPDDEs) of elliptic type. An alternate integral representation for the flux is obtained which plays an important role in the derivation of CF-scheme. We have established the stability, consistency and quadrature convergence of the proposed scheme. The scheme is successfully implemented on test problems.

Original languageEnglish
Pages (from-to)255-270
Number of pages16
JournalMathematics and Computers in Simulation
Volume165
DOIs
Publication statusPublished - 1 Nov 2019

Fingerprint

Singularly Perturbed
Fluxes
Finite volume method
Finite Volume Method
Quadrature
Integral Representation
Alternate
Test Problems

Keywords

  • Differential–difference equations
  • Finite volume methods
  • Flux
  • Integral representation of the flux
  • Singularly perturbed problems

Cite this

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title = "Complete flux scheme for elliptic singularly perturbed differential–difference equations",
abstract = "In this study, we propose a new scheme named as complete flux scheme (CF-scheme) based on the finite volume method for solving singularly perturbed differential–difference equations (SPDDEs) of elliptic type. An alternate integral representation for the flux is obtained which plays an important role in the derivation of CF-scheme. We have established the stability, consistency and quadrature convergence of the proposed scheme. The scheme is successfully implemented on test problems.",
keywords = "Differential–difference equations, Finite volume methods, Flux, Integral representation of the flux, Singularly perturbed problems",
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Complete flux scheme for elliptic singularly perturbed differential–difference equations. / Kumar, Sunil (Corresponding author); Rathish Kumar, B.V.; ten Thije Boonkkamp, J.H.M.

In: Mathematics and Computers in Simulation, Vol. 165, 01.11.2019, p. 255-270.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Complete flux scheme for elliptic singularly perturbed differential–difference equations

AU - Kumar, Sunil

AU - Rathish Kumar, B.V.

AU - ten Thije Boonkkamp, J.H.M.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - In this study, we propose a new scheme named as complete flux scheme (CF-scheme) based on the finite volume method for solving singularly perturbed differential–difference equations (SPDDEs) of elliptic type. An alternate integral representation for the flux is obtained which plays an important role in the derivation of CF-scheme. We have established the stability, consistency and quadrature convergence of the proposed scheme. The scheme is successfully implemented on test problems.

AB - In this study, we propose a new scheme named as complete flux scheme (CF-scheme) based on the finite volume method for solving singularly perturbed differential–difference equations (SPDDEs) of elliptic type. An alternate integral representation for the flux is obtained which plays an important role in the derivation of CF-scheme. We have established the stability, consistency and quadrature convergence of the proposed scheme. The scheme is successfully implemented on test problems.

KW - Differential–difference equations

KW - Finite volume methods

KW - Flux

KW - Integral representation of the flux

KW - Singularly perturbed problems

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DO - 10.1016/j.matcom.2019.03.015

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EP - 270

JO - Mathematics and Computers in Simulation

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