A fast-converging iterative scheme for solving a system of Lane–Emden equations arising in catalytic diffusion reactions

Abstract

In this paper, we present a fast-converging iterative scheme to approximate the solution of a system of Lane–Emden equations arising in catalytic diffusion reactions. In this method, the original system of differential equations subject to a Neumann boundary condition at $X = 0$ and a Dirichlet boundary condition at $X = 1$, is transformed into an equivalent system of Fredholm integral equations. The resulting system of integral equations is then efficiently treated by the optimized homotopy analysis method. A numerical example is provided to verify the effectiveness and accuracy of the method. Results have been compared with those obtained by other existing iterative schemes to show the advantage of the proposed method. It is shown that the residual error in the present method solution is seven orders of magnitude smaller than in Adomian decomposition method and five orders of magnitude smaller than in the modified Adomian decomposition method. The proposed method is very simple and accurate and it converges quickly to the solution of a given problem.