Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model
In this study, the design of a novel model based on nonlinear third-order Emden–Fowler delay differential (EF-DD) equations is presented along with two types using the sense of delay differential and standard form of the second-order EF equation. The singularity at ξ = 0 at single or multiple points...
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2020-01-01
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2020/7359242 |
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doaj-9d5586a9e930445abaf697af127e87872020-11-25T02:54:22ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/73592427359242Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential ModelJuan L.G. Guirao0Zulqurnain Sabir1Tareq Saeed2Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Santa Marina, Cartagena 30203, SpainDepartment of Mathematics and Statistics, Hazara University, Mansehra, PakistanNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, 80203, Jeddah 21589, Saudi ArabiaIn this study, the design of a novel model based on nonlinear third-order Emden–Fowler delay differential (EF-DD) equations is presented along with two types using the sense of delay differential and standard form of the second-order EF equation. The singularity at ξ = 0 at single or multiple points of each type of the designed EF-DD model are discussed. The detail of shape factors and delayed points is provided for both types of the designed third-order EF-DD model. For the verification and validation of the model, two numerical examples are presented of each case and numerical results have been performed using the artificial neural network along with the hybrid of global and local capabilities. The comparison of the obtained numerical results with the exact solutions shows the perfection and correctness of the designed third-order EF-DD model.http://dx.doi.org/10.1155/2020/7359242 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Juan L.G. Guirao Zulqurnain Sabir Tareq Saeed |
spellingShingle |
Juan L.G. Guirao Zulqurnain Sabir Tareq Saeed Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model Mathematical Problems in Engineering |
author_facet |
Juan L.G. Guirao Zulqurnain Sabir Tareq Saeed |
author_sort |
Juan L.G. Guirao |
title |
Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model |
title_short |
Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model |
title_full |
Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model |
title_fullStr |
Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model |
title_full_unstemmed |
Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model |
title_sort |
design and numerical solutions of a novel third-order nonlinear emden–fowler delay differential model |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2020-01-01 |
description |
In this study, the design of a novel model based on nonlinear third-order Emden–Fowler delay differential (EF-DD) equations is presented along with two types using the sense of delay differential and standard form of the second-order EF equation. The singularity at ξ = 0 at single or multiple points of each type of the designed EF-DD model are discussed. The detail of shape factors and delayed points is provided for both types of the designed third-order EF-DD model. For the verification and validation of the model, two numerical examples are presented of each case and numerical results have been performed using the artificial neural network along with the hybrid of global and local capabilities. The comparison of the obtained numerical results with the exact solutions shows the perfection and correctness of the designed third-order EF-DD model. |
url |
http://dx.doi.org/10.1155/2020/7359242 |
work_keys_str_mv |
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1715354953873096704 |