Solving the Lane-Emden-Fowler Type Equations of Higher Orders by the Adomian Decomposition Method

In this paper, we construct the Lane-Emden-Fowler type equations of higher orders. We study the linear and the nonlinear Lane-Emden-Fowler type equations of the third and fourth orders, where other forms can be treated in a similar manner. We use the systematic Adomian decomposition method to handle these types of equations with specified initial conditions. We confirm that the Adomian decomposition method provides an efficient algorithm for exact and approximate analytic solutions of these equations. We corroborate this study by investigating several numerical examples that emphasize initial value problems.