Approximate Analytical Solution for the Forced Korteweg-de Vries Equation
The forced Korteweg-de Vries (fKdV) equations are solved using Homotopy Analysis Method (HAM). HAM is an approximate analytical technique which provides a novel way to obtain series solutions of such nonlinear problems. It has the auxiliary parameter ℏ, where it is easy to adjust and control the con...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/795818 |
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| author | Vincent Daniel David Mojtaba Nazari Vahid Barati Faisal Salah Zainal Abdul Aziz |
| author_facet | Vincent Daniel David Mojtaba Nazari Vahid Barati Faisal Salah Zainal Abdul Aziz |
| author_sort | Vincent Daniel David |
| collection | DOAJ |
| description | The forced Korteweg-de Vries (fKdV) equations are solved using Homotopy Analysis Method (HAM). HAM is an approximate analytical technique which provides a novel way to obtain series solutions of such nonlinear problems. It has the auxiliary parameter ℏ, where it is easy to adjust and control the convergence region of the series solution. Some examples of forcing terms are employed to analyse the behaviours of the HAM solutions for the different fKdV equations. Finally, this form of HAM solution is compared with the analytical soliton-type solution of fKdV equation as derived by Zhao and Guo. The results is found to be in good agreement with Zhao and Guo. |
| format | Article |
| id | doaj-art-fbca5e31823d4bc0b0f9a26745ef96f0 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-fbca5e31823d4bc0b0f9a26745ef96f02025-02-03T01:10:16ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/795818795818Approximate Analytical Solution for the Forced Korteweg-de Vries EquationVincent Daniel David0Mojtaba Nazari1Vahid Barati2Faisal Salah3Zainal Abdul Aziz4Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, MalaysiaDepartment of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, MalaysiaDepartment of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, MalaysiaUTM Centre for Industrial and Applied Mathematics, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, MalaysiaDepartment of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, MalaysiaThe forced Korteweg-de Vries (fKdV) equations are solved using Homotopy Analysis Method (HAM). HAM is an approximate analytical technique which provides a novel way to obtain series solutions of such nonlinear problems. It has the auxiliary parameter ℏ, where it is easy to adjust and control the convergence region of the series solution. Some examples of forcing terms are employed to analyse the behaviours of the HAM solutions for the different fKdV equations. Finally, this form of HAM solution is compared with the analytical soliton-type solution of fKdV equation as derived by Zhao and Guo. The results is found to be in good agreement with Zhao and Guo.http://dx.doi.org/10.1155/2013/795818 |
| spellingShingle | Vincent Daniel David Mojtaba Nazari Vahid Barati Faisal Salah Zainal Abdul Aziz Approximate Analytical Solution for the Forced Korteweg-de Vries Equation Journal of Applied Mathematics |
| title | Approximate Analytical Solution for the Forced Korteweg-de Vries Equation |
| title_full | Approximate Analytical Solution for the Forced Korteweg-de Vries Equation |
| title_fullStr | Approximate Analytical Solution for the Forced Korteweg-de Vries Equation |
| title_full_unstemmed | Approximate Analytical Solution for the Forced Korteweg-de Vries Equation |
| title_short | Approximate Analytical Solution for the Forced Korteweg-de Vries Equation |
| title_sort | approximate analytical solution for the forced korteweg de vries equation |
| url | http://dx.doi.org/10.1155/2013/795818 |
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