Exact solutions of Laplace equation by homotopy-perturbation and Adomian decomposition methods

In this work, two powerful analytical methods, called homotopy-perturbation method (HPM) and Adomian decomposition method (ADM) are introduced to obtain the exact solutions of Laplace equation with Dirichlet and Neumann boundary conditions. The results obtained by these methods are then compared with variational iteration method (VIM). The comparison among these methods shows that although the numerical results of these methods are the same, HPM is much easier, more convenient and efficient than ADM and VIM.