Neuro-Heuristic Computational Intelligence for nonlinear Thomas-Fermi equation using trigonometric and hyperbolic approximation

Abstract We propose a computational intelligence technique to solve the nonlinear Thomas-Fermi equation for a finite interval. This technique uses an optimized approximation to reduce the error between the reference solution and optimized numerical solution with trigonometric and hyperbolic functions. Computational intelligence technique is based on optimization tools like Active Set Technique (AST), Interior Point Technique (IPT) with Sequential Quadratic Programming (SQP) through artificial neural networks (ANN). Furthermore, the proposed model results can be applied in atomic models phenomena. Numerical results showed that the optimizers provided a high level of accuracy, as well as the efficiency with marginal computational requirements infinite domain. Statistical analysis is presented, particularly fitting of normal distribution based on absolute errors (AEs) of proposed solvers and Chi-square distribution data curve fitting. It provides evidence that the present solution is highly accurate in the context of confidence bands.