Semilineární okrajové úlohy v 1D

Abstract

The Lane-Embden boundary value problem originated in astrophysics, as a model to describe the density of stars or planets. Although for selected values of the polytropic index exists an analytical solution to this problem, in most cases, the solution must be found numerically. In this thesis we will deal with the description of the solution of the Lane-Embden boundary value problem in 1D, for a polytropic index 3. This problem has no analytical solution, so after describing what all of its solutions look like, we will find them numerically. Finally, we will try to apply a similar approach to finding solution numerical to generalized Lane-Embden boundary value problem in 1D.