Traveling wave solution by differential transformation method and reduced differential transformation method
The present study further examines two recent semi-analytic methods, a reduced order of nonlinear differential transformation method (also called RDTM) and differential transformation method along with Pade approximation to discuss Jaulent–Miodek and coupled Whitham–Broer–Kaup equations. The basic i...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2016-09-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016816300680 |
| _version_ | 1818598340332355584 |
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| author | Hamed Faghanpour Ganji Mohsen Jouya Seyed Abbas Mirhosseini-Amiri Davod Domiri Ganji |
| author_facet | Hamed Faghanpour Ganji Mohsen Jouya Seyed Abbas Mirhosseini-Amiri Davod Domiri Ganji |
| author_sort | Hamed Faghanpour Ganji |
| collection | DOAJ |
| description | The present study further examines two recent semi-analytic methods, a reduced order of nonlinear differential transformation method (also called RDTM) and differential transformation method along with Pade approximation to discuss Jaulent–Miodek and coupled Whitham–Broer–Kaup equations. The basic ideas of these methods are briefly introduced and performance of the proposed methods for above mentioned equations is evaluated via comparing with exact solution. The results illustrate that the so-called DTM method, unlike RDTM, due to the presence of secular terms (similar to perturbation method), cannot be found practical for nonlinear partial differential equations (particularly in Acoustic and Wave propagation problems) even through utilizing Pade approximation; meanwhile, RDTM method, despite its simplicity and rapid convergence, assured a significant accuracy and great agreement, and thus it is fair to say that nonlinear problems together with Acoustic application which cannot be solved via Analytical methods, can be studied with reduced order of nonlinear differential transformation method. |
| first_indexed | 2024-12-16T12:02:09Z |
| format | Article |
| id | doaj.art-3e9cc04a8b8f444baad10f8f1a2052b7 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-16T12:02:09Z |
| publishDate | 2016-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-3e9cc04a8b8f444baad10f8f1a2052b72022-12-21T22:32:25ZengElsevierAlexandria Engineering Journal1110-01682016-09-015532985299410.1016/j.aej.2016.04.012Traveling wave solution by differential transformation method and reduced differential transformation methodHamed Faghanpour Ganji0Mohsen Jouya1Seyed Abbas Mirhosseini-Amiri2Davod Domiri Ganji3Department of Aerospace Engineering, Amirkabir University of Technology (Tehran Polytechnic), Postal Code, Tehran, IranDepartment of Mechanical Engineering, Babol Noshirvani University of Technology, Postal Code, Babol, IranDepartment of Economic Sciences, University of Economic Sciences, Postal Code, Tehran, IranDepartment of Mechanical Engineering, Babol Noshirvani University of Technology, Postal Code, Babol, IranThe present study further examines two recent semi-analytic methods, a reduced order of nonlinear differential transformation method (also called RDTM) and differential transformation method along with Pade approximation to discuss Jaulent–Miodek and coupled Whitham–Broer–Kaup equations. The basic ideas of these methods are briefly introduced and performance of the proposed methods for above mentioned equations is evaluated via comparing with exact solution. The results illustrate that the so-called DTM method, unlike RDTM, due to the presence of secular terms (similar to perturbation method), cannot be found practical for nonlinear partial differential equations (particularly in Acoustic and Wave propagation problems) even through utilizing Pade approximation; meanwhile, RDTM method, despite its simplicity and rapid convergence, assured a significant accuracy and great agreement, and thus it is fair to say that nonlinear problems together with Acoustic application which cannot be solved via Analytical methods, can be studied with reduced order of nonlinear differential transformation method.http://www.sciencedirect.com/science/article/pii/S1110016816300680Differential Transformation Method (DTM)Reduced DTMCoupled Jaulent–Miodek equationCoupled Whitham–Broer–Kaup equation |
| spellingShingle | Hamed Faghanpour Ganji Mohsen Jouya Seyed Abbas Mirhosseini-Amiri Davod Domiri Ganji Traveling wave solution by differential transformation method and reduced differential transformation method Alexandria Engineering Journal Differential Transformation Method (DTM) Reduced DTM Coupled Jaulent–Miodek equation Coupled Whitham–Broer–Kaup equation |
| title | Traveling wave solution by differential transformation method and reduced differential transformation method |
| title_full | Traveling wave solution by differential transformation method and reduced differential transformation method |
| title_fullStr | Traveling wave solution by differential transformation method and reduced differential transformation method |
| title_full_unstemmed | Traveling wave solution by differential transformation method and reduced differential transformation method |
| title_short | Traveling wave solution by differential transformation method and reduced differential transformation method |
| title_sort | traveling wave solution by differential transformation method and reduced differential transformation method |
| topic | Differential Transformation Method (DTM) Reduced DTM Coupled Jaulent–Miodek equation Coupled Whitham–Broer–Kaup equation |
| url | http://www.sciencedirect.com/science/article/pii/S1110016816300680 |
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