African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 231

Full Length Research Paper

A study of some systems of nonlinear partial differential equations by using Adomian and modified decomposition methods

Mohammed E. A. Rabie
  • Mohammed E. A. Rabie
  • Department of Mathematics, Faculty of Education Afif, Shaqra University, Saudi Arabia.
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Tarig M. Elzaki
  • Tarig M. Elzaki
  • Department of Mathematics, Faculty of Sciences and Arts-Alkamil, King Abdulaziz University, Jeddah-Saudi Arabia
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  •  Received: 13 February 2014
  •  Accepted: 19 August 2014
  •  Published: 03 October 2014

Abstract

In this paper, we introduce the solution of systems of nonlinear partial differential equations subject to the general initial conditions by using Adomian decomposition method (ADM) and Modified decomposition method (MDM). The proposed Adomian and Modified decomposition methods was applied to reformulated first and second order initial value problems, which leads the solution in terms of transformed variables, and the series solution will be obtained by making use of the inverse operator. The results indicate these methods to be very effective and simple.
 
Key words: System of nonlinear partial differential equations, Adomian decomposition method and modified decomposition method.