Solve third order Lane–Emden–Fowler equation by Adomian decomposition method and quartic trigonometric B-spline method
In this work, we study the Lane–Emden–Fowler equation which has a wide range of applications in astrophysics, classical and quantum mechanics. Firstly, we convert this nonlinear differential equation into an equivalent integral equation. We employ the powerful Adomian decomposition method to derive...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124000627 |
| _version_ | 1797199861153529856 |
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| author | Khalid K. Ali M.S. Mehanna Abdul-Majid Wazwaz M.A. Shaalan |
| author_facet | Khalid K. Ali M.S. Mehanna Abdul-Majid Wazwaz M.A. Shaalan |
| author_sort | Khalid K. Ali |
| collection | DOAJ |
| description | In this work, we study the Lane–Emden–Fowler equation which has a wide range of applications in astrophysics, classical and quantum mechanics. Firstly, we convert this nonlinear differential equation into an equivalent integral equation. We employ the powerful Adomian decomposition method to derive an analytical solution that will also lead to numerical solutions. Moreover, we exhibit two theorems to ensure the uniqueness of the solution of the problem and to confirm the convergence of the proposed scheme. In addition, we use quartic trigonometric B-spline as a powerful numerical method to achieve numerical solutions. Finally we present a comparison between the proposed methods to show their accuracy performance. Proper graphs are also provided to illustrate the obtained solutions. |
| first_indexed | 2024-04-24T07:22:29Z |
| format | Article |
| id | doaj.art-d2837fea71814bfe81a9a1c851536d2c |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-04-24T07:22:29Z |
| publishDate | 2024-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-d2837fea71814bfe81a9a1c851536d2c2024-04-21T04:14:34ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-06-0110100676Solve third order Lane–Emden–Fowler equation by Adomian decomposition method and quartic trigonometric B-spline methodKhalid K. Ali0M.S. Mehanna1Abdul-Majid Wazwaz2M.A. Shaalan3Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptFaculty of Engineering, MTI University, Cairo, EgyptDepartment of Mathematics, Saint Xavier University, Chicago, IL 60655, USABasic Science Department, Higher Technological Institute, Tenth of Ramadan City, Egypt; Corresponding author.In this work, we study the Lane–Emden–Fowler equation which has a wide range of applications in astrophysics, classical and quantum mechanics. Firstly, we convert this nonlinear differential equation into an equivalent integral equation. We employ the powerful Adomian decomposition method to derive an analytical solution that will also lead to numerical solutions. Moreover, we exhibit two theorems to ensure the uniqueness of the solution of the problem and to confirm the convergence of the proposed scheme. In addition, we use quartic trigonometric B-spline as a powerful numerical method to achieve numerical solutions. Finally we present a comparison between the proposed methods to show their accuracy performance. Proper graphs are also provided to illustrate the obtained solutions.http://www.sciencedirect.com/science/article/pii/S2666818124000627Lane–Emden–Fowler equationAdomian decomposition methodQuatric trigonometric B-spline method |
| spellingShingle | Khalid K. Ali M.S. Mehanna Abdul-Majid Wazwaz M.A. Shaalan Solve third order Lane–Emden–Fowler equation by Adomian decomposition method and quartic trigonometric B-spline method Partial Differential Equations in Applied Mathematics Lane–Emden–Fowler equation Adomian decomposition method Quatric trigonometric B-spline method |
| title | Solve third order Lane–Emden–Fowler equation by Adomian decomposition method and quartic trigonometric B-spline method |
| title_full | Solve third order Lane–Emden–Fowler equation by Adomian decomposition method and quartic trigonometric B-spline method |
| title_fullStr | Solve third order Lane–Emden–Fowler equation by Adomian decomposition method and quartic trigonometric B-spline method |
| title_full_unstemmed | Solve third order Lane–Emden–Fowler equation by Adomian decomposition method and quartic trigonometric B-spline method |
| title_short | Solve third order Lane–Emden–Fowler equation by Adomian decomposition method and quartic trigonometric B-spline method |
| title_sort | solve third order lane emden fowler equation by adomian decomposition method and quartic trigonometric b spline method |
| topic | Lane–Emden–Fowler equation Adomian decomposition method Quatric trigonometric B-spline method |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124000627 |
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