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.
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