A Fourth Order Finite Difference Method for the Good Boussinesq Equation
The “good” Boussinesq equation is transformed into a first order differential system. A fourth order finite difference scheme is derived for this system. The resulting scheme is analyzed for accuracy and stability. Newton’s method and linearization techniques are used to solve the resulting nonlinea...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/323260 |
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| author | M. S. Ismail Farida Mosally |
| author_facet | M. S. Ismail Farida Mosally |
| author_sort | M. S. Ismail |
| collection | DOAJ |
| description | The “good” Boussinesq equation is transformed into a first order differential system. A fourth order finite difference scheme is derived for this system. The resulting scheme is analyzed for accuracy and stability. Newton’s method and linearization techniques are used to solve the resulting nonlinear system. The exact solution and the conserved quantity are used to assess the accuracy and the efficiency of the derived method. Head-on and overtaking interactions of two solitons are also considered. The numerical results reveal the good performance of the derived method. |
| format | Article |
| id | doaj-art-8b361537b569456b859e5e12d31c1686 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8b361537b569456b859e5e12d31c16862025-02-03T05:48:16ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/323260323260A Fourth Order Finite Difference Method for the Good Boussinesq EquationM. S. Ismail0Farida Mosally1Department of Mathematics, College of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, College of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaThe “good” Boussinesq equation is transformed into a first order differential system. A fourth order finite difference scheme is derived for this system. The resulting scheme is analyzed for accuracy and stability. Newton’s method and linearization techniques are used to solve the resulting nonlinear system. The exact solution and the conserved quantity are used to assess the accuracy and the efficiency of the derived method. Head-on and overtaking interactions of two solitons are also considered. The numerical results reveal the good performance of the derived method.http://dx.doi.org/10.1155/2014/323260 |
| spellingShingle | M. S. Ismail Farida Mosally A Fourth Order Finite Difference Method for the Good Boussinesq Equation Abstract and Applied Analysis |
| title | A Fourth Order Finite Difference Method for the Good Boussinesq Equation |
| title_full | A Fourth Order Finite Difference Method for the Good Boussinesq Equation |
| title_fullStr | A Fourth Order Finite Difference Method for the Good Boussinesq Equation |
| title_full_unstemmed | A Fourth Order Finite Difference Method for the Good Boussinesq Equation |
| title_short | A Fourth Order Finite Difference Method for the Good Boussinesq Equation |
| title_sort | fourth order finite difference method for the good boussinesq equation |
| url | http://dx.doi.org/10.1155/2014/323260 |
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