A new algorithm for solving differential equations of Lane-Emden type

By Abdul-Majid Wazwaz. Applied Mathematics and Computation, 2001

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A study on the systems of the Volterra integral forms of the Lane–Emden equations by the Adomian decomposition method (2014, background): “The Lane–Emden equation of the first kind describes the temperature variation of a spherical gas cloud under the mutual attraction of its molecules and subject to the laws of thermodynamics [2,9,10].”
Differential Transformation Method for Solving Differential Equations of Lane-Emden Type (2007, methodology): “Wazwaz [4,5] has given a general study to construct exact and series solutions to Lane-Emden equations by employing the Adomian decomposition method.”
A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method (2013, methodology): “𝑥 𝑖 Exact solution Reference [1] Reference [2] Present method 0 0 0 0 0 0.01 −0.00000099 6.295572 × 10−19 5.790000 × 10−8 0 0.1 −0.0009 5.83469 × 10−13 8.409000 × 10−7 0 0.5 −0.0625 4.937685 × 10−9 2.195800 × 10−6 0 1 0 1.079378 × 10−8 8.284000 × 10−7 0 2 8 1.614569 × 10−4 1.732000 × 10−7 0 5 500 ”
Four techniques based on the B‐spline expansion and the collocation approach for the numerical solution of the Lane–Emden equation (2013, methodology): “A series solution is obtained in [19], which is as follows: y.”