Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method
The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. HAM cont...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/878349 |
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| author | Mojtaba Nazari Faisal Salah Zainal Abdul Aziz Merbakhsh Nilashi |
| author_facet | Mojtaba Nazari Faisal Salah Zainal Abdul Aziz Merbakhsh Nilashi |
| author_sort | Mojtaba Nazari |
| collection | DOAJ |
| description | The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. HAM contains the auxiliary parameter ħ, which provides us with a straightforward way to adjust and control the convergence region of the series solution. The resulted HAM solution at 8th-order and 14th-order approximation is then compared with that of the exact soliton solutions of KdV and Burgers equations, respectively, and shown to be in excellent agreement. |
| format | Article |
| id | doaj-art-fca3b6d18e4248f4af971aa4d8975d2d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-fca3b6d18e4248f4af971aa4d8975d2d2025-02-03T06:42:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/878349878349Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis MethodMojtaba Nazari0Faisal Salah1Zainal Abdul Aziz2Merbakhsh Nilashi3Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, MalaysiaDepartment of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, MalaysiaDepartment of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, MalaysiaDepartment of Computer Science and Information System, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, MalaysiaThe homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. HAM contains the auxiliary parameter ħ, which provides us with a straightforward way to adjust and control the convergence region of the series solution. The resulted HAM solution at 8th-order and 14th-order approximation is then compared with that of the exact soliton solutions of KdV and Burgers equations, respectively, and shown to be in excellent agreement.http://dx.doi.org/10.1155/2012/878349 |
| spellingShingle | Mojtaba Nazari Faisal Salah Zainal Abdul Aziz Merbakhsh Nilashi Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method Journal of Applied Mathematics |
| title | Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method |
| title_full | Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method |
| title_fullStr | Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method |
| title_full_unstemmed | Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method |
| title_short | Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method |
| title_sort | approximate analytic solution for the kdv and burger equations with the homotopy analysis method |
| url | http://dx.doi.org/10.1155/2012/878349 |
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