The method of successive approximations for exact solutions of Laplace equation and of heat-like and wave-like equations with variable coefficients (Q2910218)

The authors present the method of successive approximations (MSA or fixed-point iteration) for obtaining the exact solutions of Laplace equation with Dirichlet and Neumann boundary conditions and of heat-like and wave-like equations with variable coefficients, respectively. Results obtained by MSA are compared with those known variational iteration method, homotopy-perturbation method (HPM), homotopy analysis method, and Adomian decomposition method results. It shows that all the above mentioned methods are equivalent for Laplace, heat-like and wave-like equations.