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Zbl 1162.34005
Y ild ir im, Ahmet; Öziş, Turgut
Solutions of singular IVPs of Lane-Emden type by the variational iteration method. (English)
[J] Nonlinear Anal., Theory Methods Appl. 70, No. 6, A, 2480-2484 (2009). ISSN 0362-546X

The authors consider the following general nonlinear differential equation $Lu(x)+ Nu(x)= g(x)$, where $L$ is a linear operator, $N$ is a nonlinear operator and $g(x)$ is a known analytic function. They employ the variational iteration method obtaining the successive approximation $u_{n+1}$ by the formula $$u_{n+1}= u_n(x)+ \int^x_0 \lambda(Lu_n(\xi)+ N\widetilde u_n(\xi)- g(\xi))\,d\xi,$$ $n\ge 0$, where $\lambda$ is a general Lagrange multiplier and $\widetilde u_n$ is considered as a restricted variation, namely $\delta\widetilde u_n= 0$.
[Ludv{\'\i}k Janoš (Claremont)]

MSC 2000:: *34A12 Initial value problems for ODE
34A45 Theoretical approximation of solutions of ODE

Keywords: variational iteration method; singular IVPs; Lane-Emden type equations

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