The present work deals with the construction of a high‐order efficient technique for solving one‐dimensional nonlinear Bratu‐type and Lane‐Emden‐type problems describing various physical, chemical biological phenomena in applied science engineering. Convergence analysis method is studied. Numerical experiments are carried out to demonstrate efficiency, accuracy performance proposed method. show...

In this work we consider the existence of positive singular solutions style='text-indent:20px;'> \begin{document}$ \begin{equation} \left\{ \begin{array}{lcl} \hfill -\Delta u_1 & = \lambda_1 | \nabla u_2|^p \qquad \mbox{ in } \Omega, \\ u_2 \lambda_2 u_1|^q 0 on \partial \end{array}\right.\;\;\;\;\;\;\;(1) \end{equation} $\...

We classify solutions of finite Morse index of the fractional LaneEmden equation (−∆)su = |u|p−1u in R.

We present a useful analytic approximation to the solution of the Lane-Emden equation for infinite polytropic index the isothermal sphere. The optimized expression obtained for the density profile can be accurate to within 0.04% within 5 core-radii and to 0.1% within 10 core-radii.

In this work we propose a novel approach to integrate the Lane-Emden equations for relativistic anisotropic polytropes. We take advantage of fact that Gravitational Decoupling allows decrease number degrees freedom once well known solution Einstein field is provided as seed so after demanding polytropic equation radial pressure system automatically closed. The not only extend both isotropic or ...