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

作　　者：Waleed Al-Hayani Laheeb Alzubaidy Ahmed Entesar 

机构地区：[1]Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq [2]Department of Software Engineering, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

出　　处：《Applied Mathematics》2017年第5期693-711,共19页应用数学（英文）

摘　　要：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.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.

关 键 词：HOMOTOPY Analysis Method Genetic Algorithm EMDEN-FOWLER EQUATION Wave-Type EQUATION Adomian Polynomials Noise Terms Padé APPROXIMANTS SIMPSON Rule 

分 类 号：O1[理学—数学]