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International Journal of Differential Equations
Volume 2015, Article ID 580741, 7 pages
Research Article

Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains

1Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, Rasht, Iran
2Department of Mathematics, Rasht Branch, Islamic Azad University, P.O. Box 41335-3516, Rasht, Iran
3Department of Mathematics, Guilan Science and Research Branch, Islamic Azad University, Rasht, Iran

Received 8 July 2015; Accepted 27 August 2015

Academic Editor: Timothy R. Marchant

Copyright © 2015 Jafar Biazar and Mohsen Didgar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.