Derivation of the Adomian decomposition method using the homotopy analysis method

Adomian decomposition method has been used intensively to solve nonlinear boundary and initial value problems. It has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits. However, very little has been done to address the mathematical foundation of the method and its error analysis.In this article the mathematical derivation of the method using the homotopy analysis method is presented. In addition, an error analysis is addressed as well as the convergence criteria.