In this paper, second order non-linear ordinary differential equations of Lane-Emden type are solved using the boundary value technique. A class of second derivative backward differentiation formula is derived from some continuous multistep schemes using the multistep collocation technique. The technique transforms the numerical methods to a system of non-linear equations represented as a tridi...

In this paper, we study the fractional Henon–Lane–Emden equation associated with Hardy potential \[ (-\Delta)^{s} u - \gamma |x|^{-2s} = |x|^a |u|^{p-1} \quad \textrm{in $\mathbb{R}^{n}$}. \] Extending celebrated result of [14], obtain a classification on finite Morse index solutions to elliptic above potential. particular, critical exponent $p$ Joseph–Lundgren type is derived in supercritical ...

In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of equations. addition, finding solutions obtained equations, probability characteristics are examined. The version transformation method (DTM) is used to obtain an analytical solution close equation. Approximate expected value...

Monte Carlo (MC) method played an essential role in many areas of human activity and has found application branches physical science. This paper proposes a computational technique based on MC algorithms to solve Lane–Emden (LE) type equations. We analyze four LE equations arising astrophysics: the positive negative indices polytropic gas spheres, isothermal sphere, white dwarf equation. calcula...