Complete Flux Scheme for Elliptic Singularly Perturbed Differential-Difference Equations
This work provides a new numerical method for solving a class of challenging differential equations, but the results are limited to test problems without comparison to existing methods or quantitative improvements.
The authors propose a complete flux scheme (CFS) for solving elliptic singularly perturbed differential-difference equations, demonstrating stability, consistency, and convergence on test problems.
In this study, we propose a new scheme named as complete flux scheme (CFS) based on the finite volume method for solving singularly perturbed differential-difference equations (SPDDEs) of elliptic type. An alternate integral representation for the flux is obtained which plays an important role in the derivation of CF scheme. We have established the stability, consistency and quadrature convergence of the proposed scheme. The scheme is successfully implemented on test problems.