In this paper, a numerical technique is presented to approximate the solution of a singular perturbed delay differential equation. The continual emerge of singular perturbed delay differential equations in a mathematical model of real life applications trigger the researchers for the numerical treatment of these equations. The numerical technique is based on trigonometric cubic B-spline functions in which derivatives are approximated as a linear sum of basis functions. The obtained matrix system is solved by using the Thomas Algorithm. The convergence of the employed proposal is scrutinized and computational work is carried out on four examples to test the capability of the proposed scheme. The approximated solution is compared with the existing technique and to present the behavior of the obtained solution graphs are plotted.
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.
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