Heuristic computing technique for numerical solutions of nonlinear fourth order Emden–Fowler equation

The present study presents numerical solution of the fourth order, singular, nonlinear Emden–Fowler equation integrated computational intelligence by exploiting the efficiency of feedforward artificial neural networks (ANNs), global optimization strength of genetic algorithms (GAs) and rapid local search of sequential quadratic programming (SQP). ANN is applied to discretize the nonlinear Emden–Fowler differential equation and consequentially construct a fitness/merit function on mean squared error sense. The optimization of the decision variables of ANN to solve the multi-singular, fourth order, nonlinear Emden–Fowler equation is performed by integrating capability GAs and SQP. The proficiency of the presented approach is certified on precision, convergence and stability indices, which are further enhanced through effectiveness, significance and reliability measures on statistical data for solving three different cases of the singular systems.