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.