Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method
The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Differential Equations and Nonlinear Mechanics |
| Online Access: | http://dx.doi.org/10.1155/2008/816787 |
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| _version_ | 1832551364170874880 |
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| author | A. Sami Bataineh M. S. M. Noorani I. Hashim |
| author_facet | A. Sami Bataineh M. S. M. Noorani I. Hashim |
| author_sort | A. Sami Bataineh |
| collection | DOAJ |
| description | The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given. |
| format | Article |
| id | doaj-art-dc038e9ab618454182ae1e1b647b0130 |
| institution | Kabale University |
| issn | 1687-4099 1687-4102 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Differential Equations and Nonlinear Mechanics |
| spelling | doaj-art-dc038e9ab618454182ae1e1b647b01302025-02-03T06:01:39ZengWileyDifferential Equations and Nonlinear Mechanics1687-40991687-41022008-01-01200810.1155/2008/816787816787Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis MethodA. Sami Bataineh0M. S. M. Noorani1I. Hashim2School of Mathematical Sciences, Faculty of Science and Tecnology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaSchool of Mathematical Sciences, Faculty of Science and Tecnology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaSchool of Mathematical Sciences, Faculty of Science and Tecnology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaThe time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.http://dx.doi.org/10.1155/2008/816787 |
| spellingShingle | A. Sami Bataineh M. S. M. Noorani I. Hashim Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method Differential Equations and Nonlinear Mechanics |
| title | Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method |
| title_full | Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method |
| title_fullStr | Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method |
| title_full_unstemmed | Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method |
| title_short | Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method |
| title_sort | series solution of the multispecies lotka volterra equations by means of the homotopy analysis method |
| url | http://dx.doi.org/10.1155/2008/816787 |
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