Application of Local Fractional Homotopy Perturbation Method in Physical Problems
Nonlinear phenomena have important effects on applied mathematics, physics, and issues related to engineering. Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an a...
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| Format: | Article |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/2108973 |
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| author | Nabard Habibi Zohre Nouri |
| author_facet | Nabard Habibi Zohre Nouri |
| author_sort | Nabard Habibi |
| collection | DOAJ |
| description | Nonlinear phenomena have important effects on applied mathematics, physics, and issues related to engineering. Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. The perturbation method is a wave equation solution using HPM compared with the Fourier series method, and both methods results are good agreement. The percentage of error of ux,t with α=1 and 0.33, t =0.1 sec, between the present research and Yong-Ju Yang study for x≥0.6 is less than 10. Also, the % error for x≥0.5 in α=1 and 0.33, t =0.3 sec, is less than 5, whereas for α=1 and 0.33, t =0.8 and 0.7 sec, the % error for x≥0.4 is less than 8. |
| format | Article |
| id | doaj-art-9dda5e0424694aeea7df219d60d38092 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9dda5e0424694aeea7df219d60d380922025-02-03T06:43:31ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/21089732108973Application of Local Fractional Homotopy Perturbation Method in Physical ProblemsNabard Habibi0Zohre Nouri1Department of Mechanical Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj 6617715175, IranDepartment of Mechanical Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj 6617715175, IranNonlinear phenomena have important effects on applied mathematics, physics, and issues related to engineering. Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. The perturbation method is a wave equation solution using HPM compared with the Fourier series method, and both methods results are good agreement. The percentage of error of ux,t with α=1 and 0.33, t =0.1 sec, between the present research and Yong-Ju Yang study for x≥0.6 is less than 10. Also, the % error for x≥0.5 in α=1 and 0.33, t =0.3 sec, is less than 5, whereas for α=1 and 0.33, t =0.8 and 0.7 sec, the % error for x≥0.4 is less than 8.http://dx.doi.org/10.1155/2020/2108973 |
| spellingShingle | Nabard Habibi Zohre Nouri Application of Local Fractional Homotopy Perturbation Method in Physical Problems Advances in Mathematical Physics |
| title | Application of Local Fractional Homotopy Perturbation Method in Physical Problems |
| title_full | Application of Local Fractional Homotopy Perturbation Method in Physical Problems |
| title_fullStr | Application of Local Fractional Homotopy Perturbation Method in Physical Problems |
| title_full_unstemmed | Application of Local Fractional Homotopy Perturbation Method in Physical Problems |
| title_short | Application of Local Fractional Homotopy Perturbation Method in Physical Problems |
| title_sort | application of local fractional homotopy perturbation method in physical problems |
| url | http://dx.doi.org/10.1155/2020/2108973 |
| work_keys_str_mv | AT nabardhabibi applicationoflocalfractionalhomotopyperturbationmethodinphysicalproblems AT zohrenouri applicationoflocalfractionalhomotopyperturbationmethodinphysicalproblems |