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Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method. (English) Zbl 1209.65104
Summary: The homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the time-dependent Emden-Fowler type equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of 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:
 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 35Q53 KdV equations (Korteweg-de Vries equations)
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