Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden–Fowler model

Abstract

The aim of the current study is to present the numerical solutions of a nonlinear second-order coupled Emden–Fowler equation by developing a neuro-swarming-based computing intelligent solver. The feedforward artificial neural networks (ANNs) are used for modelling, and optimization is carried out by the local/global search competences of particle swarm optimization (PSO) aided with capability of interior-point method (IPM), i.e., ANNs-PSO-IPM. In ANNs-PSO-IPM, a mean square error-based objective function is designed for nonlinear second-order coupled Emden–Fowler (EF) equations and then optimized using the combination of PSO-IPM. The inspiration to present the ANNs-PSO-IPM comes with a motive to depict a viable, detailed and consistent framework to tackle with such stiff/nonlinear second-order coupled EF system. The ANNs-PSO-IP scheme is verified for different examples of the second-order nonlinear-coupled EF equations. The achieved numerical outcomes for single as well as multiple trials of ANNs-PSO-IPM are incorporated to validate the reliability, viability and accuracy.

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“…Sabir et al. 36 proposed a neuro swarm computational heuristic model which integrated neural networks with particle swarm optimization to solve nonlinear coupled Emden–Fowler models. At the same time, they 37 combined genetic algorithm (GA) with sequential quadratic programming (SQP) to optimize Goodman neural networks (GNNs) used for solving a class of singular periodic nonlinear differential systems (SP-NDS) in nuclear physics.…”