Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method

In this paper, we consider the coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. First, we utilize systems of Volterra integral forms of the Lane–Emden equations and derive the modified recursion scheme for the components of the decomposition series solutions. The numerical results display that the Adomian decomposition method gives reliable algorithm for analytic approximate solutions of these systems. The error analysis of the sequence of the analytic approximate solutions can be performed by using the error remainder functions and the maximal error remainder parameters, which demonstrate an approximate exponential rate of convergence.