Reduced differential transform method for nonlinear integral member of Kadomtsev–Petviashvili hierarchy differential equations

Mohamed, Mohamed S.; Gepreel, Khaled A.

doi:10.1016/j.joems.2016.04.007

	Reduced differential transform method for nonlinear integral member of Kadomtsev–Petviashvili hierarchy differential equations
Journal of the Egyptian Mathematical Society
Volume 25, Issue 1, 2017, Page 1-7 PDF (1.39 MB)
DOI: 10.1016/j.joems.2016.04.007
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Authors
Mohamed S. Mohamed ¹^{, 2}; Khaled A. Gepreel ³^{, 2}
¹Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, Egypt
²Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia
³Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
Abstract
The main objective of this paper is to use the reduced differential to transform method (RDTM) for find- ing the analytical approximate solutions of two integral members of nonlinear Kadomtsev–Petviashvili (KP) hierarchy equations. Comparing the approximate solutions which obtained by RDTM with the exact solutions to show that the RDTM is quite accurate, reliable and can be applied for many other non- linear partial differential equations. The RDTM produces a solution with few and easy computation. This method is a simple and efficient method for solving the nonlinear partial differential equations. The anal- ysis shows that our analytical approximate solutions converge very rapidly to the exact solutions.


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