An Algorithm for Solving Initial Value Problems Using Laplace Adomian Decomposition Method

The Adomian Decomposition Method (ADM) has been applied to a wide class of problems in physics, biology and chemical reactions. The method provides the solution in a rapid convergent series with computable terms. This method was successfully applied to nonlinear differential delay equations [1], a nonlinear dynamic systems [2], the heat equation [3,4], the wave equation [5], coupled nonlinear partial differential equations [6,7], linear and nonlinear integro-differential equations [8] and Airy’s equation [9]. Different modifications of this method and their applications are given in [10-13]. The Laplace Adomian Decomposition Method (LADM) is a combination of ADM and placeLaplace transforms. This method was successfully used for solving Bratu and Duffing equations in [14,15]. In this paper, we developed a symbolic algorithm to find the solution of { anx n dny dxn + an−1xn−1 dn−1y dxn−1 + · · ·+ a1x dx + a0y + F (y) = G(x) y(x0) = α0, y ′(x0) = α1, . . . , y(x0) = αn (1)