A neuro-swarming intelligent heuristic for second-order nonlinear Lane–Emden multi-pantograph delay differential system

Abstract The current study is related to present a novel neuro-swarming intelligent heuristic for nonlinear second-order Lane–Emden multi-pantograph delay differential (NSO-LE-MPDD) model by applying the approximation proficiency of artificial neural networks (ANNs) and local/global search capabilities particle swarm optimization (PSO) together with efficient/quick interior-point (IP) approach, i.e., ANN-PSOIP scheme. In designed scheme, merit function proposed using mean square error sense along continuous mapping ANNs NSO-LE-MPDD model. training these nets capable integrated competence PSO IP inspiration approach instigates reliable, steadfast, consistent arrangement relates strength soft computing handle such inspiring classifications. Furthermore, statistical soundings different operators certify convergence, accurateness, precision