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In this study, we propose a new scheme named as complete flux scheme (CFS)based on the finite volume method for solving singularly perturbeddifferential-difference equations (SPDDEs) of elliptic type. An alternateintegral representation for the flux is obtained which plays an important rolein the derivation of CF scheme. We have established the stability, consistencyand quadrature convergence of the proposed scheme. The scheme is successfullyimplemented on test problems.

Complete Flux Scheme for Elliptic Singularly Perturbed Differential-Difference Equations