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Solutions of singular IVPs of Lane-Emden type by the variational iteration method. (English) Zbl 1162.34005
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 $\delta\widetilde u_n= 0$.

MSC:
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34A45Theoretical approximation of solutions of ODE
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