文章基本信息

标题：Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains
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作者：Jafar Biazar ; Mohsen Didgar
期刊名称：International Journal of Differential Equations
印刷版ISSN：1687-9643
电子版ISSN：1687-9651
出版年度：2015
卷号：2015
DOI：10.1155/2015/580741
出版社：Hindawi Publishing Corporation
摘要：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.