WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
Analytical Solution of Two Model Equations for Shallow Water Waves and their Extended Model Equations by Adomian’s Decomposition and He’s Variational Iteration Methods
Author:
Abstract: In this paper two model equations for shallow water waves and their extended models were considered. Adomian’s decomposition method (ADM) and variational iteration method (VIM) have been employed to solve them. Large classes of linear and nonlinear differential equations, both ordinary as well as partial, can be solved by the ADM. The decomposition method provides an effective procedure for analytical solution of a wide and general class of dynamical systems representing real physical problems. This method efficiently works for initial- value or boundary-value problems and for linear or nonlinear, ordinary or partial differential equations and even for stochastic systems. The variational iteration method (VIM) established in (1999) by He is thoroughly used by many researchers to handle linear and nonlinear models. Finally the results of ADM and VIM methods have been compared and it is shown that the results of the VIM method are in excellent agreement with results of ADM method and the obtained solutions are shown graphically.