Complete flux scheme for parabolic singularly perturbed differential-difference equations

Sunil Kumar; Bayya Venkatesulu Rathish Kumar; J.H.M. ten Thije Boonkkamp

doi:10.1002/num.22325

Complete flux scheme for parabolic singularly perturbed differential-difference equations

Sunil Kumar (Corresponding author)
, Bayya Venkatesulu Rathish Kumar
, J.H.M. ten Thije Boonkkamp

Center for Analysis, Scientific Computing and Applications

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

2 Citations (Scopus)

184 Downloads (Pure)

Abstract

In this study, we investigate the concept of the complete flux (CF) obtained as a solution to a local boundary value problem (BVP) for a given parabolic singularly perturbed differential‐difference equation (SPDDE) with modified source term to propose an efficient complete flux‐finite volume method (CF‐FVM) for parabolic SPDDE which is μ‐ and ϵ‐uniform method where μ, ϵ are shift and perturbation parameters, respectively. The proposed numerical method is shown to be consistent, stable, and convergent and has been successfully implemented on three test problems.

Original language	English
Pages (from-to)	790-804
Number of pages	15
Journal	Numerical Methods for Partial Differential Equations
Volume	35
Issue number	2
Early online date	3 Dec 2018
DOIs	https://doi.org/10.1002/num.22325
Publication status	Published - 1 Mar 2019

Keywords

differential-difference equations, finite volume method, flux, integral representation of the flux, singularly perturbed problems

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10.1002/num.22325

published versionFinal published version, 1.99 MBLicence: TAVERNE

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abstract = "In this study, we investigate the concept of the complete flux (CF) obtained as a solution to a local boundary value problem (BVP) for a given parabolic singularly perturbed differential‐difference equation (SPDDE) with modified source term to propose an efficient complete flux‐finite volume method (CF‐FVM) for parabolic SPDDE which is μ‐ and ϵ‐uniform method where μ, ϵ are shift and perturbation parameters, respectively. The proposed numerical method is shown to be consistent, stable, and convergent and has been successfully implemented on three test problems.",

keywords = "differential-difference equations, finite volume method, flux, integral representation of the flux, singularly perturbed problems",

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Complete flux scheme for parabolic singularly perturbed differential-difference equations. / Kumar, Sunil (Corresponding author); Rathish Kumar, Bayya Venkatesulu; ten Thije Boonkkamp, J.H.M.
In: Numerical Methods for Partial Differential Equations, Vol. 35, No. 2, 01.03.2019, p. 790-804.

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

TY - JOUR

T1 - Complete flux scheme for parabolic singularly perturbed differential-difference equations

AU - Kumar, Sunil

AU - Rathish Kumar, Bayya Venkatesulu

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

PY - 2019/3/1

Y1 - 2019/3/1

N2 - In this study, we investigate the concept of the complete flux (CF) obtained as a solution to a local boundary value problem (BVP) for a given parabolic singularly perturbed differential‐difference equation (SPDDE) with modified source term to propose an efficient complete flux‐finite volume method (CF‐FVM) for parabolic SPDDE which is μ‐ and ϵ‐uniform method where μ, ϵ are shift and perturbation parameters, respectively. The proposed numerical method is shown to be consistent, stable, and convergent and has been successfully implemented on three test problems.

AB - In this study, we investigate the concept of the complete flux (CF) obtained as a solution to a local boundary value problem (BVP) for a given parabolic singularly perturbed differential‐difference equation (SPDDE) with modified source term to propose an efficient complete flux‐finite volume method (CF‐FVM) for parabolic SPDDE which is μ‐ and ϵ‐uniform method where μ, ϵ are shift and perturbation parameters, respectively. The proposed numerical method is shown to be consistent, stable, and convergent and has been successfully implemented on three test problems.

KW - differential-difference equations, finite volume method, flux, integral representation of the flux, singularly perturbed problems

U2 - 10.1002/num.22325

DO - 10.1002/num.22325

M3 - Article

SN - 0749-159X

VL - 35

SP - 790

EP - 804

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 2

ER -

Complete flux scheme for parabolic singularly perturbed differential-difference equations

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