The use of the Adomian decomposition method for solving a parabolic equation with temperature overspecification

Certain types of physical problems can be modelled by a parabolic partial differential equation with temperature overspecification. In this work, the Adomian decomposition method is used to solve the two-dimensional (or three-dimensional) parabolic partial differential equation subject to the overspecification at a point in the spatial domain. This analytic technique can also be used to provide a numerical approximation for the problem without linearization or discretization. The Adomian decomposition procedure does not need to solve any linear or nonlinear system of algebraic equations. It finds the solution in a rapid convergent series. Some theoretical behaviours of the method are investigated. To support the theoretical discussion and show the superiority of the method, two test problems are given and the numerical results are presented.