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Computational scheme for a differential difference equation with a large delay in convection term

Erla Srinivas, Kolloju Phaneendra

International Journal of Applied Mechanics and Engineering

2023

Vol. 28, no. 2

34--48

A computational scheme for the solution of layer behaviour differential equation involving a large delay in the derivative term is devised using numerical integration. If the delay is greater than the perturbation parameter, the layer structure of the solution is no longer preserved, and the solution oscillates. A numerical method is devised with the support of a specific kind of mesh in order to reduce the error and regulate the layered structure of the solution with a fitting parameter. The scheme is discussed for convergence. The maximum errors in the solution are tabulated and compared to other methods in the literature to verify the accuracy of the numerical method. Using this specific kind of mesh with and without the fitting parameter, we also studied the layer and oscillatory behavior of the solution with a large delay.

Robust numerical method for singularly perturbed differential equations with large delay

Abdulla Murad Ibrahim, Duressa Gemechis File, Debela Habtamu Garoma

Demonstratio Mathematica

2021

Vol. 54, nr 1

576--589

In this paper, a singularly perturbed differential equation with a large delay is considered. The considered problem contains a large delay parameter on the reaction term. The solution of the problem exhibits the interior layer due to the delay parameter and the strong right boundary layer due to the small perturbation parameter ε. The resulting singularly perturbed problem is solved using the fitted non-polynomial spline method. The stability and parameter uniform convergence of the proposed method is proved. To validate the applicability of the scheme, two model problems of the variable coefficient are considered for numerical experimentation.