Neuro-swarms intelligent computing using Gudermannian kernel for solving a class of second order Lane-Emden singular nonlinear model

Abstract

The present work is to design a novel Neuro swarm computing standards using artificial intelligence scheme to exploit the Gudermannian neural networks (GNN)accomplished with global and local search ability of particle swarm optimization (PSO) and sequential quadratic programming scheme (SQPS), called as GNN-PSO-SQPS to solve a class of the second order Lane-Emden singular nonlinear model (SO-LES-NM). The suggested intelligent computing solver GNN-PSO-SQPS using the Gudermannian kernel are unified with the configuration of the hidden layers of GNN of differential operators for solving the SO-LES-NM. An error based fitness function (FF) applying the differential form of the differential model and corresponding boundary conditions. The FF is optimized together with the combined heuristics of PSO-SQPS. Three problems of the SO-LES-NM are solved to validate the correctness, effectiveness and competence of the designed GNN-PSO-SQPS. The performance of the GNN-PSO-SQPS through statistical operators is tested to check the constancy, convergence and precision.

Keywords

• lane-emden singular system
• gudermannian neural networks
• sequential quadratic scheme
• gudermannian kernel
• numerical results
• particle swarm optimization