### International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

###### Quintic B-Spline Technique for Numerical Treatment of Third Order Singular Perturbed Delay Differential Equation

Mandeep Kaur Vaid
Department of Mathematics, Lovely Professional University, Phagwara, Punjab, India.

Geeta Arora
Department of Mathematics, Lovely Professional University, Phagwara, Punjab, India.

;
Accepted on August 07, 2019

Abstract

In this paper, a class of third order singularly perturbed delay differential equation with large delay is considered for numerical treatment. The considered equation has discontinuous convection-diffusion coefficient and source term. A quintic trigonometric B-spline collocation technique is used for numerical simulation of the considered singularly perturbed delay differential equation by dividing the domain into the uniform mesh. Further, uniform convergence of the solution is discussed by using the concept of Hall error estimation and the method is found to be of first-order convergent. The existence of the solution is also established. Computation work is carried out to validate the theoretical results.

Keywords- Quintic trigonometric spline, Error estimate, Perturbed equation, Delay.

Citation

Vaid, M. K., & Arora, G. (2019). Quintic B-Spline Technique for Numerical Treatment of Third Order Singular Perturbed Delay Differential Equation. International Journal of Mathematical, Engineering and Management Sciences, 4(6), 1471-1482. https://dx.doi.org/10.33889/IJMEMS.2019.4.6-116.

Conflict of Interest

The authors confirm that this article contents have no conflict of interest.

Acknowledgements

The authors would like to express their sincere thanks to the editor and referee for their valuable suggestions towards the improvement of the paper.

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