TY - JOUR
T1 - Complete flux scheme for elliptic singularly perturbed differential–difference equations
AU - Kumar, Sunil
AU - Rathish Kumar, B.V.
AU - ten Thije Boonkkamp, J.H.M.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - In this study, we propose a new scheme named as complete flux scheme (CF-scheme) 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.
AB - In this study, we propose a new scheme named as complete flux scheme (CF-scheme) 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.
KW - Differential–difference equations
KW - Finite volume methods
KW - Flux
KW - Integral representation of the flux
KW - Singularly perturbed problems
UR - http://www.scopus.com/inward/record.url?scp=85064702202&partnerID=8YFLogxK
U2 - 10.1016/j.matcom.2019.03.015
DO - 10.1016/j.matcom.2019.03.015
M3 - Article
AN - SCOPUS:85064702202
SN - 0378-4754
VL - 165
SP - 255
EP - 270
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -