Numerical treatment for the nonlinear fifth kind of multi-singular differential model: a neuro-swarming approach

Abstract

In this study, a numerical scheme is proposed for the fifth order (FO) singular differential model (SDM), FO-SDM. The solutions of the singular form of the differential models are always considered difficult to solve and huge important in astrophysics. A neural network study together with the hybrid combination of global particle swarm optimization and local sequential quadratic programming schemes is provided to find the numerical simulations of the FO-SDM. An objective function is constructed using the differential FO-SDM along with the boundary conditions. The correctness of the scheme is observed by providing the comparison of the obtained and exact solutions. The justification of the proposed scheme is authenticated in terms of absolute error (AE), which is calculated in good measures for solving the FO-SDM. The efficiency and reliability of the stochastic approach are observed using the statistical performances to solve the FO-SDM.