New Numerical Solution For Solving Nonlinear Singular Thomas-Fermi Differential Equation

作者：Parand Kourosh^*; Delkhosh Mehdi

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2017, 24(3): 457-476.

DOI：10.36045/bbms/1506477694

• Thomas-Fermi equation
• Collocation method
• Fractional order of the Chebyshev functions
• Semi-infinite domain
• Singular points
• Nonlinear ODE

In this paper, the nonlinear singular Thomas-Fermi differential equation on a semi-infinite domain for neutral atoms is solved by using the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) of the first kind. First, this collocation method reduces the solution of this problem to the solution of a system of nonlinear algebraic equations. Second, using solve a system of nonlinear equations, the initial value for the unknown parameter L is calculated, and finally, the value of L to increase the accuracy of the initial slope is improved and the value of y'(0) = -1.588071022611375312718684509 is calculated. The comparison with some numerical solutions shows that the present solution is highly accurate.

• 出版日期2017-9