Solving a novel designed second order nonlinear Lane-Emden delay differential model using the heuristic techniques

The aim of the present study is to present a new model based on the nonlinear singular second order delay differential equation of Lane-Emden type and numerically solved by using the heuristic technique. Four different examples are presented based on the designed model and numerically solved by using artificial neural networks optimized by the global search, local search methods and their hybrid combinations, respectively, named as genetic algorithm (GA), sequential quadratic programming (SQP) and GA-SQP. The numerical results of the designed model are compared for the proposed heuristic technique with the exact/explicit results that demonstrate the performance and correctness. Moreover, statistical investigations/assessments are presented for the accuracy and performance of the designed model implemented with heuristic methodology. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study presents a new model based on the nonlinear singular second order delay differential equation of Lane-Emden type, which is numerically solved using heuristic technique. Four different examples are solved using artificial neural networks optimized by genetic algorithm (GA), sequential quadratic programming (SQP), and GA-SQP. The numerical results are compared with the exact results to demonstrate performance and correctness, and statistical investigations are presented to assess the accuracy and performance of the designed model implemented with heuristic methodology.