Analytical solutions to a quasilinear differential equation related to the Lane-Emden equation of the second kind

作者：Van Gorder Robert A^*

来源：Celestial Mechanics and Dynamical Astronomy, 2011, 109(2): 137-145.

DOI：10.1007/s10569-010-9318-y

• Lane-Emden equation of the second kind
• Bonnor-Ebert gas spheres
• Perturbation method
• delta-expansion method
• Quasilinear differential equation

We apply the delta-expansion method to a transformed Lane-Emden equation. The results are then transformed back, and we recover analytical solutions to the Lane-Emden equation of the second kind (which describes Bonnor-Ebert gas spheres) in a special case. The rapid convergence of the method results in qualitatively accurate solutions in relatively few iterations, as we see when we compare the obtained analytical solutions to numerical results.

• 出版日期2011-2