A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions
This work provides a new numerical technique for solving singular boundary value problems on semi-infinite domains, which is of interest to researchers in applied mathematics and computational physics.
The paper introduces a fractional order of rational Bessel functions collocation method to solve the Thomas-Fermi equation on a semi-infinite domain without truncation or transformation, achieving accurate and efficient numerical results compared to existing methods.
In this paper, the fractional order of rational Bessel functions collocation method (FRBC) to solve Thomas-Fermi equation which is defined in the semi-infinite domain and has singularity at $x = 0$ and its boundary condition occurs at infinity, have been introduced. We solve the problem on semi-infinite domain without any domain truncation or transformation of the domain of the problem to a finite domain. This approach at first, obtains a sequence of linear differential equations by using the quasilinearization method (QLM), then at each iteration solves it by FRBC method. To illustrate the reliability of this work, we compare the numerical results of the present method with some well-known results in other to show that the new method is accurate, efficient and applicable.