Least Square Homotopy Perturbation Method for Ordinary Differential Equations
In this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). The proposed scheme is teste...
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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/10.1155/2021/7059194 |
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| _version_ | 1832546072023531520 |
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| author | Mubashir Qayyum Imbsat Oscar |
| author_facet | Mubashir Qayyum Imbsat Oscar |
| author_sort | Mubashir Qayyum |
| collection | DOAJ |
| description | In this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). The proposed scheme is tested against various linear and nonlinear BVPs (second to seventh order DEs). Validity of the obtained solutions is confirmed by finding absolute errors. To analyze the efficiency of the proposed scheme, tested problems have also been solved through HPM and results are compared with LSHPM. Furthermore, obtained results are also compared with other numerical schemes available in literature. Analysis reveals that LSHPM is a consistent and effective scheme which can be used for more complex BVPs in science and engineering. |
| format | Article |
| id | doaj-art-988a490f07074a728fcf6e6884d627b2 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-988a490f07074a728fcf6e6884d627b22025-02-03T07:24:01ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/70591947059194Least Square Homotopy Perturbation Method for Ordinary Differential EquationsMubashir Qayyum0Imbsat Oscar1National University of Computer and Emerging Sciences FAST, Lahore, PakistanNational University of Computer and Emerging Sciences FAST, Lahore, PakistanIn this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). The proposed scheme is tested against various linear and nonlinear BVPs (second to seventh order DEs). Validity of the obtained solutions is confirmed by finding absolute errors. To analyze the efficiency of the proposed scheme, tested problems have also been solved through HPM and results are compared with LSHPM. Furthermore, obtained results are also compared with other numerical schemes available in literature. Analysis reveals that LSHPM is a consistent and effective scheme which can be used for more complex BVPs in science and engineering.http://dx.doi.org/10.1155/2021/7059194 |
| spellingShingle | Mubashir Qayyum Imbsat Oscar Least Square Homotopy Perturbation Method for Ordinary Differential Equations Journal of Mathematics |
| title | Least Square Homotopy Perturbation Method for Ordinary Differential Equations |
| title_full | Least Square Homotopy Perturbation Method for Ordinary Differential Equations |
| title_fullStr | Least Square Homotopy Perturbation Method for Ordinary Differential Equations |
| title_full_unstemmed | Least Square Homotopy Perturbation Method for Ordinary Differential Equations |
| title_short | Least Square Homotopy Perturbation Method for Ordinary Differential Equations |
| title_sort | least square homotopy perturbation method for ordinary differential equations |
| url | http://dx.doi.org/10.1155/2021/7059194 |
| work_keys_str_mv | AT mubashirqayyum leastsquarehomotopyperturbationmethodforordinarydifferentialequations AT imbsatoscar leastsquarehomotopyperturbationmethodforordinarydifferentialequations |