Abstract
In physical science, nonlinear singular Lane-Emden and pantograph delay differential equations (LE-PDDEs) have abundant applications and thus are of great interest for the researchers. The presented investigation is related to the development of a new application of intelligent computing for the solution of the LE-PDDEs-based system introduced recently by merging the essence of delay differential equation of Pantograph type and standard second-order Lane-Emden equation. Intelligent computing is exploited through Levenberg-Marquardt backpropagation networks (LMBNs) and Bayesian regularization backpropagation networks (BRBNs) to provide the solutions to nonlinear second-order LE-PDDEs. The performance of design LMBNs and BRBNs is substantiated on three different case studies through comparative analysis from known exact/explicit solutions. The correctness of the designed solvers for LE-PDDEs is further certified by accomplishing through assessment on error histograms, regression measures and index of mean squared error.