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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 793685, 7 pages
Research Article

Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

Department of Mechanical Engineering, Salmas Branch, Islamic Azad University, Salmas, Iran

Received 15 February 2014; Accepted 6 June 2014; Published 19 June 2014

Academic Editor: Onesimo Hernandez-Lerma

Copyright © 2014 Nemat Dalir. 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.


Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.