The nonlinear partial differential equation governing on the mentioned system has been investigated by a simple and innovative method which we have named it Akbari-Ganji's Method or AGM. It is notable that this method has been compounded by Laplace transform theorem in order to covert the partial differential equation governing on the afore-mentioned system to an ODE and then the yielded equation has been solved conveniently by this new approach (AGM). One of the most important reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in heat transfer science but also in different fields of study such as solid mechanics, fluid mechanics, chemical engineering, etc. in comparison with the other methods is as follows: Obviously, according to the order of differential equations, we need boundary conditions so in the case of the number of boundary conditions is less than the order of the differential equation, this method can create additional new boundary conditions in regard to the own differential equation and its derivatives. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods.
An observation problem for the Bessel differential operator
