A new analytical technique for solving Lane - Emden type equations arising in astrophysics

Abstract

Lane -Emden type equations are nonlinear differential equations which represent many scientific phenomena in astrophysics and mathematical physics. In this study, a new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and performance of the method. This technique provides us to adjust the convergence regions when necessary.Comparing different methods reveals that the proposed method is highly accurate and has great potential to be a new kind of powerful analytical tool for Lane-Emden type equations.

On the Solution of KdV-Like Equations by the Optimal Perturbation Iteration Technique

“…The approximate solution of order m can be obtained after putting 01 ,, PP into the last one of the equations (12). For more detailed information about OPIM, please see [13][14][15][16][17][18][19].…”

On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

“…The solutions of the Volterra and Fredholm type integral equations [36], ordinary differential equation and systems [37] and the solutions of ordinary fractional differential equations [38] have given by the present method. Modification of the PIA has been also introduced by Bildik and Deniz [43][44][45].…”

Two-step collocation methods for two-dimensional Volterra integral equations of the second kind

“…For example, in [14], the differential transform method has been considered for VIEs. Recently, many new methods have been presented to solve some types of differential and integral equations [1,8,9]. Also, multi-step collocation methods have been proposed for one-dimensional VIEs of the second kind in some interesting works [4][5][6].…”