Journal of Function Spaces
Volume 2014, Article ID 790714, 5 pages
http://dx.doi.org/10.1155/2014/790714
Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method
1Mathematics Department, Faculty of Sciences for Girls, King Abdulaziz University, Jeddah, Saudi Arabia
2Mathematics Department, Faculty of Sciences and Arts, King Abdulaziz University, P.O. Box 110, Alkamil 21931, Saudi Arabia
Received 17 December 2013; Revised 14 February 2014; Accepted 24 February 2014; Published 26 March 2014
Academic Editor: Leszek Olszowy
Copyright © 2014 Eman M. A. Hilal and Tarig M. Elzaki. 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.
Abstract
The aim of this study is to give a good strategy for solving some linear and nonlinear partial differential equations in engineering and physics fields, by combining Laplace transform and the modified variational iteration method. This method is based on the variational iteration method, Laplace transforms, and convolution integral, introducing an alternative Laplace correction functional and expressing the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions.