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Homotopy analysis method for singular IVPs of Emden-Fowler type. (English) Zbl 1221.65197
Summary: Approximate and/or exact analytical solutions of singular initial value problems (IVPs) of the Emden-Fowler type in the second-order ordinary differential equations (ODEs) are obtained by the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. It is shown that the solutions obtained by the Adomian decomposition method (ADM) and the homotopy-perturbation method (HPM) are only special cases of the HAM solutions.

##### MSC:
 65L99 Numerical methods for ordinary differential equations 34A45 Theoretical approximation of solutions to ordinary differential equations
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