A Reliable Treatment for Nonlinear Differential Equations
In this paper, we use the concept of homotopy, Laplace transform, and He’s polynomials, to propose the auxiliary Laplace homotopy parameter method (ALHPM). We construct a homotopy equation consisting on two auxiliary parameters for solving nonlinear differential equations, which switch nonlinear ter...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6659479 |
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| author | H. R. Marasi M. Sedighi H. Aydi Y. U. Gaba |
| author_facet | H. R. Marasi M. Sedighi H. Aydi Y. U. Gaba |
| author_sort | H. R. Marasi |
| collection | DOAJ |
| description | In this paper, we use the concept of homotopy, Laplace transform, and He’s polynomials, to propose the auxiliary Laplace homotopy parameter method (ALHPM). We construct a homotopy equation consisting on two auxiliary parameters for solving nonlinear differential equations, which switch nonlinear terms with He’s polynomials. The existence of two auxiliary parameters in the homotopy equation allows us to guarantee the convergence of the obtained series. Compared with numerical techniques, the method solves nonlinear problems without any discretization and is capable to reduce computational work. We use the method for different types of singular Emden–Fowler equations. The solutions, constructed in the form of a convergent series, are in excellent agreement with the existing solutions. |
| format | Article |
| id | doaj-art-8eab1ecc8e2f4358b47829133546c0d7 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-8eab1ecc8e2f4358b47829133546c0d72025-02-03T01:20:38ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/6659479A Reliable Treatment for Nonlinear Differential EquationsH. R. Marasi0M. Sedighi1H. Aydi2Y. U. Gaba3Department of Applied MathematicsDepartment of MathematicsUniversité de SousseDepartment of Mathematics and Applied MathematicsIn this paper, we use the concept of homotopy, Laplace transform, and He’s polynomials, to propose the auxiliary Laplace homotopy parameter method (ALHPM). We construct a homotopy equation consisting on two auxiliary parameters for solving nonlinear differential equations, which switch nonlinear terms with He’s polynomials. The existence of two auxiliary parameters in the homotopy equation allows us to guarantee the convergence of the obtained series. Compared with numerical techniques, the method solves nonlinear problems without any discretization and is capable to reduce computational work. We use the method for different types of singular Emden–Fowler equations. The solutions, constructed in the form of a convergent series, are in excellent agreement with the existing solutions.http://dx.doi.org/10.1155/2021/6659479 |
| spellingShingle | H. R. Marasi M. Sedighi H. Aydi Y. U. Gaba A Reliable Treatment for Nonlinear Differential Equations Journal of Mathematics |
| title | A Reliable Treatment for Nonlinear Differential Equations |
| title_full | A Reliable Treatment for Nonlinear Differential Equations |
| title_fullStr | A Reliable Treatment for Nonlinear Differential Equations |
| title_full_unstemmed | A Reliable Treatment for Nonlinear Differential Equations |
| title_short | A Reliable Treatment for Nonlinear Differential Equations |
| title_sort | reliable treatment for nonlinear differential equations |
| url | http://dx.doi.org/10.1155/2021/6659479 |
| work_keys_str_mv | AT hrmarasi areliabletreatmentfornonlineardifferentialequations AT msedighi areliabletreatmentfornonlineardifferentialequations AT haydi areliabletreatmentfornonlineardifferentialequations AT yugaba areliabletreatmentfornonlineardifferentialequations AT hrmarasi reliabletreatmentfornonlineardifferentialequations AT msedighi reliabletreatmentfornonlineardifferentialequations AT haydi reliabletreatmentfornonlineardifferentialequations AT yugaba reliabletreatmentfornonlineardifferentialequations |