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

• 作者: Ahmed Entesar Laheeb Alzubaidy Waleed Al-Hayani
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: HOMOTOPY Analysis Method Genetic Algorithm EMDEN-FOWLER EQUATION Wave-Type EQUATION Adomian Polynomials Noise Terms Padé APPROXIMANTS SIMPSON Rule
• 年，卷（期）: 2017,（5）
• 页码范围: 693-711
• 页数: 19页
• 分类号: O1

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.