Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains
We combine the Adomian decomposition method (ADM) and Adomian’s asymptotic decomposition method (AADM) for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2015/580741 |
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| _version_ | 1832562598531301376 |
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| author | Jafar Biazar Mohsen Didgar |
| author_facet | Jafar Biazar Mohsen Didgar |
| author_sort | Jafar Biazar |
| collection | DOAJ |
| description | We combine the Adomian decomposition method (ADM) and Adomian’s asymptotic decomposition method (AADM) for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation. We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance. |
| format | Article |
| id | doaj-art-4cfb1c90689e4eada06e257707ea2f24 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-4cfb1c90689e4eada06e257707ea2f242025-02-03T01:22:12ZengWileyInternational Journal of Differential Equations1687-96431687-96512015-01-01201510.1155/2015/580741580741Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended DomainsJafar Biazar0Mohsen Didgar1Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, Rasht, IranDepartment of Mathematics, Rasht Branch, Islamic Azad University, P.O. Box 41335-3516, Rasht, IranWe combine the Adomian decomposition method (ADM) and Adomian’s asymptotic decomposition method (AADM) for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation. We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance.http://dx.doi.org/10.1155/2015/580741 |
| spellingShingle | Jafar Biazar Mohsen Didgar Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains International Journal of Differential Equations |
| title | Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains |
| title_full | Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains |
| title_fullStr | Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains |
| title_full_unstemmed | Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains |
| title_short | Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains |
| title_sort | numerical solution of riccati equations by the adomian and asymptotic decomposition methods over extended domains |
| url | http://dx.doi.org/10.1155/2015/580741 |
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