| 總結: | The Goursat partial differential equation is a hyperbolic partial differential equation which arises in various fields of study. Many approaches have been suggested to approximate the solution of the Goursat partial differential equation such as the finite difference method, Runge-Kutta method, finite element method, differential transform method, and modified variational iteration method. These methods traditionally focus on numerical differentiation approaches including the forward and central differences in deriving the schemes. In this paper we have developed a new scheme to solve the Goursat partial differential equation that applies the Adomian decomposition (ADM) associated with the Newton-Cotes formula for approximating the integration terms. The homogeneous linear Goursat problems are examined and the new scheme supplied quantitatively reliable results for these types of problems. The accuracy level of the results obtained indicates the superiority of these new schemes over standard scheme that applied to the Goursat partial differential equation. © 2013 AIP Publishing LLC.
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