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In this paper, a new technique of Hybrid of Adomian polynomial is developed by the substitution of a One-step method of Taylor's series approximation of orders I and II into the nonlinear part of Adomian decomposition method .This yield a new Taylor series of Adomian Decomposition Method in the nonlinear part. The applications of the modified new hybrid polynomial to some classical problems give results that approximate the analytical solutions of the problems with minimal errors. Keyword:doi:10.5539/jmr.v7n1p102 fatcat:berti5r2wbgyrcerylcfrwt3pu