Table of Contents
International Journal of Partial Differential Equations
Volume 2014, Article ID 607259, 6 pages
Research Article

Improvement of the Modified Decomposition Method for Handling Third-Order Singular Nonlinear Partial Differential Equations with Applications in Physics

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

Received 4 June 2014; Accepted 9 October 2014; Published 6 November 2014

Academic Editor: Athanasios N. Yannacopoulos

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.


The modified decomposition method (MDM) is improved by introducing new inverse differential operators to adapt the MDM for handling third-order singular nonlinear partial differential equations (PDEs) arising in physics and mechanics. A few case-study singular nonlinear initial-value problems (IVPs) of third-order PDEs are presented and solved by the improved modified decomposition method (IMDM). The solutions are compared with the existing exact analytical solutions. The comparisons show that the IMDM is effectively capable of obtaining the exact solutions of the third-order singular nonlinear IVPs.