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.
Highlights
The frequent emerge of singular perturbed delay differential equations (SPDDE) in every field of science and technology has triggered the researchers for numerical treatment of these equations
These equations involve two sensitive parameters: perturbation (ε) and retarded(δ) parameter. The study of these differential equations is a stiff job for the researchers due to startlingadapt of the solution at boundary as ε → 0, and such variation in solution at the boundary is well known as boundary layer
A class of third order SPDDE for ordinary delay differential equations with large delay is considered with discontinuous convection-diffusion coefficient and source term
Summary
The frequent emerge of singular perturbed delay differential equations (SPDDE) in every field of science and technology has triggered the researchers for numerical treatment of these equations. The delay differential equations are the result of mathematical models of the real-life problems in various fields. One such model exists in study of the development of the bearing of the population of a system of organisms. One such mathematical model of the singular biological system is proposed by Zhang et al (2016) by considering the delay parameter into account.
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