Fractional order of rational Jacobi functions for solving the non-linear singular Thomas-Fermi equation

Abstract

In this paper, a new method based on Fractional order of Rational Jacobi (FRJ) functions is proposed that utilizes quasilinearization method to solve non-linear singular Thomas-Fermi equation on unbounded interval \([0,\infty)\). The equation is solved without domain truncation and variable changing. First, the quasilinearization method is used to convert the equation to the sequence of linear ordinary differential equations. Then, by using the FRJs collocation method the equations are solved. For the evaluation, comparison with some numerical solutions shows that the proposed solution is highly accurate.