Fatemeh Rooholamini - Department of Computer Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran.
Alireza Afzal Aghaei - Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C. Tehran, Iran
Seyed Mohammad Hossein Hasheminejad - Department of Computer Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran
Reza Azmi - Department of Computer Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran
Sarah Soltani - Department of Computer Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran

This paper presents a novel approach for tackling the Lane-Emden equation, a significant nonlinear differential equation of paramount importance in the realms of physics and astrophysics. We employ the Chimp optimization algorithm in conjunction with Chebyshev polynomials to devise an innovative solution strategy. Inspired by the behavioral patterns of chimpanzees, the Chimp algorithm is harnessed to optimize the Chebyshev polynomial approximations, thereby transforming the Lane-Emden equation into an unconstrained optimization problem. Our method's effectiveness is demonstrated through a series of numerical experiments, showcasing its capability to precisely solve the Lane-Emden equation across various polytropic indices.

Metaheuristic Algorithms, Chimp optimization algorithm, Lane-Emden differential equations