Abstract
In this paper we like to explore the full power of Adomian decomposition method (ADM), specially its symbolic capability. We will demonstrate the standard ADM and ADM with integration factor to compute explicit closed form solutions of first order scalar partial differential equations with unprescribed initial conditions, and even with parameters. These features are those numerical methods fail to do. Our examples include linear/nonlinear, constant/variable coefficients and homogeneous/nonhomogeneous equations. The method of characteristics is also tested and compared with these two ADM methods. We conclude that ADM is excellent among all existing methods.
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