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On the numerical solution of differential equations of Lane-Emden type. (English) Zbl 1193.65151
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:
65L99Numerical methods for ODE
34A45Theoretical approximation of solutions of ODE
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