Quintic B-Spline Method for Numerical Solution of Second Order Singularly Perturbed Delay Differential Equations

Lodhi, Ram Kishun; Malge, Shilpa

doi:10.22034/cmde.2024.61474.2650

Quintic B-Spline Method for Numerical Solution of Second Order Singularly Perturbed Delay Differential Equations

Articles in Press

Document Type : Research Paper

Authors

Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune, India.

10.22034/cmde.2024.61474.2650

Abstract

This article presents a quintic B-spline method to find an approximate solution of the second-order singularly perturbed differential equation in which convection term occurs with negative shift. The proposed method gives rise to a penta-diagonal linear system. Thomas algorithm is employed to solve the obtained system of equations. The error estimate, existence and uniqueness of the solution are proved. 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 convergence. The effect of the delay parameter on the boundary region is also discussed in the example.

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