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Complete flux scheme for parabolic singularly perturbed differential‐difference equations
Authors:Sunil Kumar  Bayya Venkatesulu Rathish Kumar  Johannes Hendrikus Maria Ten Thije Boonkkamp
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 ?‐uniform method where μ, ? 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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