Complete flux scheme for parabolic singularly perturbed differential-difference equations

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

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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.
Originele taal-2Engels
Pagina's (van-tot)790-804
Aantal pagina's15
TijdschriftNumerical Methods for Partial Differential Equations
Volume35
Nummer van het tijdschrift2
Vroegere onlinedatum3 dec 2018
DOI's
StatusGepubliceerd - 1 mrt 2019

Vingerafdruk

Differential-difference Equations
Difference equations
Singularly Perturbed
Boundary value problems
Numerical methods
Fluxes
Parameter Perturbation
Source Terms
Test Problems
Boundary Value Problem
Numerical Methods
Concepts

Citeer dit

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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, Nr. 2, 01.03.2019, blz. 790-804.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

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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.

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