Algorithm

Nonlinear programming

Physics

Mathematical optimization

Engineering

Quadratic equation

Aerospace engineering

Artificial intelligence

Nonlinear system

Heuristic

Sequential quadratic programming

Geometry

Mathematics

Computer science

Artificial neural network

Correctness

Quantum mechanics

Differential evolution

Quadratic programming

Genetic algorithm

Differential (mechanical device)

Applied Soft Computing

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.

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