Abstract
In this paper, the Adomian's decomposition method is effectively implemented to establish an analytic solution and a reliable numerical approximation to the Goursat partial differential equation. Linear and nonlinear Goursat examples are examined, and the method supplied quantitatively reliable results for these types of problems. The accuracy level of the results obtained indicates the superiority of the decomposition method over existing numerical methods that were applied to the Goursat problem.
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