Computational Approach to Solving a Layered Behaviour Differential Equation with Large Delay Using Quadrature Scheme
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Department of Mathematics, University College of Science, Osmania University, Hyderabad, India
Department of Mathematics, Malla Reddy Engineering College, Hyderabad
Online publication date: 2022-12-03
Publication date: 2022-12-01
International Journal of Applied Mechanics and Engineering 2022;27(4):117-137
This paper deals with the computational approach to solving the singularly perturbed differential equation with a large delay in the differentiated term using the two-point Gaussian quadrature. If the delay is bigger than the perturbed parameter, the layer behaviour of the solution is destroyed, and the solution becomes oscillatory. With the help of a special type mesh, a numerical scheme consisting of a fitting parameter is developed to minimize the error and to control the layer structure in the solution. The scheme is studied for convergence. Compared with other methods in the literature, the maximum defects in the approach are tabularized to validate the competency of the numerical approach. In the suggested technique, we additionally focused on the effect of a large delay on the layer structure or oscillatory behaviour of the solutions using a special form of mesh with and without a fitting parameter. The effect of the fitting parameter is demonstrated in graphs to show its impact on the layer of the solution.
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