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Method for solving nonlinear initial value problems by combining homotopy perturbation and reproducing kernel Hilbert space methods. (English) Zbl 1187.34012

Summary: The main idea of this paper is to present an algorithm for computing the solutions of singular initial value problems including Lane-Emden-type equations of the form

u '' (x)+k 1 a(x)u ' (t)+k 2 b(x)u(t)+f(x,u)=g(x),0<x1,u(0)=α,u ' (0)=β,

where α,β,k 1 ,k 2 are real constants, a(x), b(x) ar continuous and maybe a(0)=0, b(0)=0, f(x,y) is a continuous real valued function, and g(x)C(0,1], i.e., the case when the function g(x) may be undefined at the origin.

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