Eur. Phys. J. Plus (2018) 133: 364
https://doi.org/10.1140/epjp/i2018-12153-4

Regular Article

A new stochastic computing paradigm for the dynamics of nonlinear singular heat conduction model of the human head

¹ Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock, Pakistan
² Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan
³ Department of Computer Science and Engineering, HITEC University, Texila Rawalpindi, Pakistan
⁴ Department of Mathematics, Cankaya University, Ankara, Turkey
⁵ Institute of Space Sciences, Magurele-Bucharest, Romania

^* e-mail: Muhammad.asif@ciit-attock.edu.pk

Received: 12 June 2018
Accepted: 19 July 2018
Published online: 13 September 2018

Abstract

Bio-inspired computing approaches are effective to solve a variety of dynamical problems. The strength of these stochastic solvers is exploited for the numerical treatment of a nonlinear heat conduction model of the human head using artificial neural networks (ANNs), genetic algorithms (GAs), active-set technique (AST), and their hybrids. The universal function approximation competencies of unsupervised ANNs are utilized in constructing the mathematical model of the problem by defining an error function in the mean squared sense. The training of the design parameters of ANN models is made with global search brilliance of GAs, viably local search with AST and hybrid approach GA-AST. The results of the proposed schemes are determined in terms of temperature profiles by considering variants of the problem with different Biot numbers, metabolic thermogenesis slope parameters and thermogenesis heat production factors. The correctness, effectiveness and convergence of the proposed approaches are also ascertained through statistics.