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Complete flux scheme for parabolic singularly perturbed differential‐difference equations
Author(s) -
Kumar Sunil,
Rathish Kumar Bayya Venkatesulu,
Ten Thije Boonkkamp Johannes Hendrikus Maria
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22325
Subject(s) - mathematics , mathematical analysis , parabolic partial differential equation , perturbation (astronomy) , boundary value problem , flux (metallurgy) , finite difference method , singular perturbation , finite volume method , differential equation , partial differential equation , mechanics , physics , materials science , quantum mechanics , metallurgy
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.