In this paper, we discuss the application of the Adomian's decomposition method (ADM) for solving Laplace equations with Dirichlet boundary conditions. Among other advantages, the ADM does not require meshes and easily creates general solutions for coupled systems of linear and nonlinear partial differential equations. However, the imposition of boundary conditions is not simple in realistic domains. Here we propose an approach to overcome this difficult, apply our techniques in classical problems of Electrostatics, and compare the obtained results to equivalent solutions calculated by the Finite Element Method.
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