A new heuristic computational solver for nonlinear singular Thomas-Fermi system using evolutionary optimized cubic splines

In the present work, a new stochastic computing technique based on evolutionary cubic spline method (CSM) is introduced for solving nonlinear singular Thomas-Fermi system arising in atomic physics. The concept of cubic splines interpolation is engaged with an evolutionary optimization technique based on genetic algorithms (GAs) hybrid with sequential quadratic programming (SQP) to develop a proposed methodology, CSM-GASQP, that can solve nonlinear differential equations, and GA produces the optimized value for the coefficients of cubic splines, while SQP is used for rapid local refinements. The developed method CSM-GASQP for different lengths of the splines is applied effectively to solve the Thomas-Fermi equation for number of scenarios. Results show that proposed evolutionary paradigm CSM-GASQP is an effective, alternate, accurate, and reliable stochastic numerical solver for stiff nonlinear singular Thomas-Fermi systems.