Analytical approach for computation of exact and analytic approximate solutions to the system of Lane-Emden-Fowler type equations arising in astrophysics

摘要

In this paper, we study the system of Lane-Emden-Fowler type equations which model many phenomena in mathematical physics and astrophysics. The equivalent Volterra integral forms of system of Lane-Emden-Fowler equations is considered. A reliable algorithm based on the optimal homotopy analysis method is employed for the exact and analytic approximate solutions to the Volterra integral forms of the system of equations. Convergence and error analysis of the proposed method are also discussed. The analytical results show that the present method gives a reliable algorithm for the approximate series solutions and the exact solutions of these systems.