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Zbl 1193.65151
Vanani, S.Karimi; Aminataei, A.
On the numerical solution of differential equations of Lane-Emden type. (English)
[J] Comput. Math. Appl. 59, No. 8, 2815-2820 (2010). ISSN 0898-1221

Summary: A numerical method which produces an approximate polynomial solution is presented for solving Lane-Emden equations as singular initial value problems. Firstly, we use an integral operator and convert Lane-Emden equations into integral equations. Then, we convert the acquired integral equation into a power series. Finally, transforming the power series into Padé series form, we obtain an approximate polynomial of arbitrary order for solving Lane-Emden equations. The advantages of using the proposed method are presented. Then, an efficient error estimation for the proposed method is also introduced and finally some experiments and their numerical solutions are given; and comparing between the numerical results obtained from the other methods, we show the high accuracy and efficiency of the proposed method.

MSC 2000:: *65L99 Numerical methods for ODE
34A45 Theoretical approximation of solutions of ODE

Keywords: Lane-Emden equations; arbitrary order; power series; Padé series

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