Abstract
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.
Highlights
Mathematical modeling of numerous real life phenomenon results in ordinary differential equations which help the researchers to solve environmental issues such as pollution, cyber security and so on
The perturbation parameter ε is multiplied with higher order derivative term of singular perturbed delay differential equations (SPDDE) and arises due to the clampdown in the small parameter of the physical systems which in turns reduce the order of system as ε → 0
Delay parameter exists in the argument of the reaction term which appears due to the participation of feedback which is obligatory in order to avoid a rickety state
Summary
Mathematical modeling of numerous real life phenomenon results in ordinary differential equations which help the researchers to solve environmental issues such as pollution, cyber security and so on One such model that discussed the water pollutants and outturn as a system of nonlinear ordinary differential equation is given by Shah et al (2018). Mathematical subject involving the study of singular perturbed delay differential equations (SPDDE) has become a full-fledged research with a long background. These equations are prominent for their extended implementations in every part of science and engineering. Kanth and Kumar (2018) proposed a parametric spline scheme for a class of nonlinear SPDDE With this motivation, trigonometric cubic B-spline collocation method is used to solve singular perturbed delay differential equations.
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