University of Tabriz Computational Methods for Differential Equations 2345-3982 14 1 2026 11 01 Quintic B-spline method for numerical solution of second-order singularly perturbed delay differential equations 36 49 18759 10.22034/cmde.2024.61474.2650 EN Shilpa Malge Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune, India. Ram Kishun Lodhi Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune, India. Journal Article 2024 05 01 This article presents a quintic B-spline method to find an approximate solution of the second-order singularly perturbed differential equation in which the convection term occurs with a negative shift. The proposed method gives rise to a pentadiagonal linear system. Thomas' algorithm is employed to solve the obtained system of equations. The method’s convergence is examined through truncation error analysis, and the existence and uniqueness of the solution are also established. Maximum absolute error is tabulated for two numerical examples, proving the proposed method’s efficiency. Graphs are drawn to show the behavior of the solution. A comparative study shows that the obtained solution is better than the previous solutions in the literature. The method is found to be fourth-order convergent. The effect of the delay parameter on the boundary region is also discussed in the example. Singularly perturbed delay differential equation Boundary value problem Spline methods Quintic B-spline method Existence and uniqueness uniform mesh Convergence https://cmde.tabrizu.ac.ir/article_18759_fd898012f3fbdbae82ad7f3dd7667b31.pdf