University of Tabriz Computational Methods for Differential Equations 2345-3982 10 2 2022 04 01 Uniformly convergent fitted operator method for singularly perturbed delay differential equations 502 518 12977 10.22034/cmde.2021.41166.1789 EN Mesfin Mekuria Woldaregay Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia. Habtamu Garoma Debela Department of Mathematics, Jimma University, Jimma, Ethiopia. Gemechis File Duressa Department of Mathematics, Jimma University, Jimma, Ethiopia. Journal Article 2020 08 14 This paper deals with the numerical treatment of singularly perturbed delay differential equations having a delay on the first derivative term. The solution of the considered problem exhibits boundary layer behavior on the left or right side of the domain depending on the sign of the convective term. The term with the delay is approximated using Taylor series approximation, resulting in an asymptotically equivalent singularly perturbed boundary value problem. The uniformly convergent numerical scheme is developed using exponentially fitted finite difference method. The stability of the scheme is investigated using solution bound. The uniform convergence of the scheme is discussed and proved. Numerical examples are considered to validate the theoretical analysis.  https://cmde.tabrizu.ac.ir/article_12977_8b19ddf041d364852e4352dfa5cd2e42.pdf