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Dehghan, M. and Shakeri, F. (2008) Approximate Solution of a Differential Equation Arising in Astrophysics Using the Variational Iteration Method. New Astronomy, 13, 53-59.

has been cited by the following article:

• TITLE: Analytical Solution for the Time-Dependent Emden-Fowler Type of Equations by Homotopy Analysis Method with Genetic Algorithm

  AUTHORS: Waleed Al-Hayani, Laheeb Alzubaidy, Ahmed Entesar

  KEYWORDS: Homotopy Analysis Method, Genetic Algorithm, Emden-Fowler Equation, Wave-Type Equation, Adomian Polynomials, Noise Terms, Padé Approximants, Simpson Rule

  JOURNAL NAME: Applied Mathematics, Vol.8 No.5, May 25, 2017

  ABSTRACT: In this paper, Homotopy Analysis method with Genetic Algorithm is presented and used to obtain an analytical solution for the time-dependent Emden-Fowler type of equations and wave-type equation with singular behavior at x = 0. The advantage of this single global method employed to present a reliable framework is utilized to overcome the singularity behavior at the point x = 0 for both models. The method is demonstrated for a variety of problems in one and higher dimensional spaces where approximate-exact solutions are obtained. The results obtained in all cases show the reliability and the efficiency of this method.