Computational Approach to Solving a Layered Behaviour Differential Equation with Large Delay Using Quadrature Scheme
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...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2022-12-01
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| Series: | International Journal of Applied Mechanics and Engineering |
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| Online Access: | https://www.ijame-poland.com/Computational-Approach-to-Solving-a-Layered-Behaviour-Differential-Equation-with,166643,0,2.html |
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| author | Amala Pandi Lalu Mudavath Phaneendra Kolloju |
| author_facet | Amala Pandi Lalu Mudavath Phaneendra Kolloju |
| author_sort | Amala Pandi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:33:41Z |
| format | Article |
| id | doaj.art-a45f9d400e7f428db7365b22d19b1d21 |
| institution | Directory Open Access Journal |
| issn | 1734-4492 2353-9003 |
| language | English |
| last_indexed | 2024-03-12T16:33:41Z |
| publishDate | 2022-12-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | International Journal of Applied Mechanics and Engineering |
| spelling | doaj.art-a45f9d400e7f428db7365b22d19b1d212023-08-08T15:05:01ZengUniversity of Zielona GóraInternational Journal of Applied Mechanics and Engineering1734-44922353-90032022-12-0127411713710.2478/ijame-2022-0054166643Computational Approach to Solving a Layered Behaviour Differential Equation with Large Delay Using Quadrature SchemeAmala Pandi0Lalu Mudavath1Phaneendra Kolloju2Department of Mathematics, University College of Science, Osmania University, Hyderabad, IndiaDepartment of Mathematics, Malla Reddy Engineering College, HyderabadDepartment of Mathematics, University College of Science, Osmania University, Hyderabad, IndiaThis 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.https://www.ijame-poland.com/Computational-Approach-to-Solving-a-Layered-Behaviour-Differential-Equation-with,166643,0,2.htmlsingularly perturbed delay differential equationlayer behaviorfitting parametergaussian quadrature |
| spellingShingle | Amala Pandi Lalu Mudavath Phaneendra Kolloju Computational Approach to Solving a Layered Behaviour Differential Equation with Large Delay Using Quadrature Scheme International Journal of Applied Mechanics and Engineering singularly perturbed delay differential equation layer behavior fitting parameter gaussian quadrature |
| title | Computational Approach to Solving a Layered Behaviour Differential Equation with Large Delay Using Quadrature Scheme |
| title_full | Computational Approach to Solving a Layered Behaviour Differential Equation with Large Delay Using Quadrature Scheme |
| title_fullStr | Computational Approach to Solving a Layered Behaviour Differential Equation with Large Delay Using Quadrature Scheme |
| title_full_unstemmed | Computational Approach to Solving a Layered Behaviour Differential Equation with Large Delay Using Quadrature Scheme |
| title_short | Computational Approach to Solving a Layered Behaviour Differential Equation with Large Delay Using Quadrature Scheme |
| title_sort | computational approach to solving a layered behaviour differential equation with large delay using quadrature scheme |
| topic | singularly perturbed delay differential equation layer behavior fitting parameter gaussian quadrature |
| url | https://www.ijame-poland.com/Computational-Approach-to-Solving-a-Layered-Behaviour-Differential-Equation-with,166643,0,2.html |
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