THE NEW ADM–PADÉ TECHNIQUE FOR THE GENERALIZED EMDEN–FOWLER EQUATIONS

In this paper, the Emden–Fowler equations are investigated by employing the Adomian decomposition method (ADM) and the Pade approximant. By using the new type of Adomian polynomials proposed by Randolph C. Rach in 2008, our obtained solution series converges much faster than the regular ADM solution of the same order. Meanwhile, we note that the solutions obtained by using the new ADM–Pade technique have much higher accuracy and larger convergence domain than those obtained by using the regular ADM together with the Pade technique. Finally, comparison of our new obtained solutions are given with those existing exact ones graphically to illustrate the validity and the promising potential of the new ADM–Pade technique for solving nonlinear problems.

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