基于有理贝塞尔函数分数阶的非线性托马斯-费米方程新求解方法
A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions
AI总结：
本文提出基于有理贝塞尔函数分数阶的求解方法，用于求解定义在半无限域且在x=0处有奇点的托马斯-费米方程，无需域截断或变换，通过拟线性化方法获得线性微分方程序列，并利用该方法进行求解，验证了方法的准确性、高效性和适用性。
摘要：
本文介绍了基于有理贝塞尔函数分数阶的求解方法（FRBC），用于求解定义在半无限域且在x=0处有奇点的托马斯-费米方程，其边界条件出现在无穷远处。我们无需对问题域进行截断或变换为有限域即可解决该问题。该方法首先通过拟线性化方法（QLM）获得一系列线性微分方程，然后在每次迭代中使用FRBC方法求解。为了验证该工作的可靠性，我们比较了本文方法的数值结果与一些已知结果，证明了新方法的准确性、高效性和适用性。
英文摘要：
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.
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