一种TFD方程的数值解法及一些常见元素的电子密度求解

A Solution of TFD Equation and the Numerical Computation of the Electron Density for Some Common Elements

四阶Runge-Kutta法是工程计算中常用的一种求解微分方程的数值计算方法,具有精度高,易收敛等优点。本文在Feynman等人计算方法的基础上,用经典的四阶Runge-Kutta法来求解Thomas-Fermi-Dirac(TFD)方程,进一步提高原计算方法的计算精度。利用该方法求出了元素Cu的TFD方程数值解并计算出一些常见元素在Wigner-Seitz半径处的电子密度。

Fourth order Runge-Kutta method is commonly used to solve the differential equations in engineering due to its high precision and easy convergence. In this paper, based on the Feynman et al.＇s calculated method, the classical fourth order Runge-Kutta method was applied to solve the Thomas-Fermi-Dirac （TFD） equation and more accurate results have been obtained. Using this method, the numerical solution of the TFD equation for the element Cu was solved, and the electron density values of some common elements at the Wigner-Seitz radius were calculated.