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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)+ 0 x λ(Lu n (ξ)+Nu ˜ n (ξ)-g(ξ))dξ,

n0, where λ is a general Lagrange multiplier and u ˜ n is considered as a restricted variation, namely δu ˜ n =0.

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