A generator of Lie point symmetries admitted by a Lane–Emden equation of the second-kind for arbitrary shape factor k is used to determine invariant boundary conditions admitted by the equation. The generator of Lie point symmetries is then used to reduce the order of the Lane–Emden equation. A phase plane analysis of the reduced equation indicates that the stability of the invariant boundary c...

In this study, a high-order compact finite difference method is used to solve Lane–Emden equations with various boundary conditions. The norm use first-order scheme approximate Neumann and Robin conditions, but that compromises the accuracy of entire scheme. As result, new higher-order schemes for approximating conditions are developed in work. We test applicability performance using different ...

<p style='text-indent:20px;'>Ordinary differential equations are converted into a constrained optimization problems to find their approximate solutions. In this work, an algorithm is proposed by applying particle swarm (PSO) solution of ODEs based on expansion approximation. Since many cases linear and nonlinear have singularity point, Padé approximant which fractional employed for more a...