Eur. Phys. J. Plus (2022) 137: 782
https://doi.org/10.1140/epjp/s13360-022-02978-z

Regular Article

Computational heuristics for solving nonlinear singular Thomas–Fermi equation with genetic exponential collocation algorithm

¹ Department of Physics, AIR University, PAF Complex, E-9, 44000, Islamabad, Pakistan
² Department of Computer and Information Sciences, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad, Pakistan
³ Department of Physics and Applied Mathematics, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad, Pakistan

^e rubinanm@yahoo.com, rubina.nasir@mail.au.edu.pk

Received: 16 December 2021
Accepted: 19 June 2022
Published online: 7 July 2022

Abstract

A novel approach of Genetic Exponential Collocation Algorithm (GECA) is reported for the solution of nonlinear singular Thomas–Fermi equation (TFE) arising in the statistical estimates of various models in atomic physics, astrophysics and solid-state physics. GECA exploits the strength of Genetic Algorithm (GA) as global search mechanism along with exponential collocation method for the solution of differential equation. In this mechanism, TFE is transformed into coupled system of nonlinear equations by exponential collocation technique and fitness is calculated in terms of residual. Fitness in turn is minimized exploiting GA in the feasible search space. The designed scheme is then applied to solve TFE for three scenarios involving different input values of independent parameter. Performance of the proposed mechanism is evaluated in terms of statistical measures. The effectiveness of the proposed scheme is consistently achieved by the optimally converging values of the statistical performance indices for appropriate number of independent executions. The solutions obtained by the proposed GECA are in good agreement with the published data. Further, this study is extended for even larger range of independent variable. The results show that the developed technique is computationally efficient, reliable and robust.