Reliable iterative methods for 1D Swift–Hohenberg equation
In this paper, the nonlinear problem of the 1 D Swift-Hohenberg equation (S-HE) has been solved by using five reliable iterative methods. The first one is the Daftardar-Jafari method namely (DJM), the second method is the Temimi-Ansari method namely (TAM), the third method is the Banach contraction...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2020-01-01
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| Series: | Arab Journal of Basic and Applied Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/25765299.2020.1715129 |
| _version_ | 1818965123185770496 |
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| author | Majeed A. AL-Jawary Othman Mahdi Salih |
| author_facet | Majeed A. AL-Jawary Othman Mahdi Salih |
| author_sort | Majeed A. AL-Jawary |
| collection | DOAJ |
| description | In this paper, the nonlinear problem of the 1 D Swift-Hohenberg equation (S-HE) has been solved by using five reliable iterative methods. The first one is the Daftardar-Jafari method namely (DJM), the second method is the Temimi-Ansari method namely (TAM), the third method is the Banach contraction method namely (BCM), the fourth method is the Adomian decomposition method namely (ADM) and finally the fifth method is the Variational iteration method (VIM) to obtain the approximate solutions. In this work, we discussed and applied these iterative methods to solve the S-HE and compared them. In addition, the fixed-point theorem was given to illustrate the convergence of the five methods. To illustrate the accuracy and efficiency of the five methods, the maximum error remainder was calculated since the exact solution is unknown. The results showed that the five iterative methods are accurate, reliable, time saver and effective. All the iterative processes in this paper implemented in MATHEMATICA®11. |
| first_indexed | 2024-12-20T13:12:00Z |
| format | Article |
| id | doaj.art-0fb58dfb99044686939701928c998c37 |
| institution | Directory Open Access Journal |
| issn | 2576-5299 |
| language | English |
| last_indexed | 2024-12-20T13:12:00Z |
| publishDate | 2020-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj.art-0fb58dfb99044686939701928c998c372022-12-21T19:39:39ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992020-01-01271566610.1080/25765299.2020.17151291715129Reliable iterative methods for 1D Swift–Hohenberg equationMajeed A. AL-Jawary0Othman Mahdi Salih1Department of Mathematics, College of Education for Pure Science Ibn Al-Haitham, University of BaghdadDepartment of Mathematics, College of Education for Pure Science Ibn Al-Haitham, University of BaghdadIn this paper, the nonlinear problem of the 1 D Swift-Hohenberg equation (S-HE) has been solved by using five reliable iterative methods. The first one is the Daftardar-Jafari method namely (DJM), the second method is the Temimi-Ansari method namely (TAM), the third method is the Banach contraction method namely (BCM), the fourth method is the Adomian decomposition method namely (ADM) and finally the fifth method is the Variational iteration method (VIM) to obtain the approximate solutions. In this work, we discussed and applied these iterative methods to solve the S-HE and compared them. In addition, the fixed-point theorem was given to illustrate the convergence of the five methods. To illustrate the accuracy and efficiency of the five methods, the maximum error remainder was calculated since the exact solution is unknown. The results showed that the five iterative methods are accurate, reliable, time saver and effective. All the iterative processes in this paper implemented in MATHEMATICA®11.http://dx.doi.org/10.1080/25765299.2020.1715129approximate solutioniterative methodsnonlinear partial differential equationssemi-analytical solutionswift-hohenberg equation |
| spellingShingle | Majeed A. AL-Jawary Othman Mahdi Salih Reliable iterative methods for 1D Swift–Hohenberg equation Arab Journal of Basic and Applied Sciences approximate solution iterative methods nonlinear partial differential equations semi-analytical solution swift-hohenberg equation |
| title | Reliable iterative methods for 1D Swift–Hohenberg equation |
| title_full | Reliable iterative methods for 1D Swift–Hohenberg equation |
| title_fullStr | Reliable iterative methods for 1D Swift–Hohenberg equation |
| title_full_unstemmed | Reliable iterative methods for 1D Swift–Hohenberg equation |
| title_short | Reliable iterative methods for 1D Swift–Hohenberg equation |
| title_sort | reliable iterative methods for 1d swift hohenberg equation |
| topic | approximate solution iterative methods nonlinear partial differential equations semi-analytical solution swift-hohenberg equation |
| url | http://dx.doi.org/10.1080/25765299.2020.1715129 |
| work_keys_str_mv | AT majeedaaljawary reliableiterativemethodsfor1dswifthohenbergequation AT othmanmahdisalih reliableiterativemethodsfor1dswifthohenbergequation |