In this work we deal with the method of polynomial collocation and use it to solve boundary value problems in ordinary differential equations. Collocation was implemented in the open domain Matlab code bvpsuite which has been developed at the Institute for Analysis and Scientific Computing, Vienna University of Technology. This implementation includes an error estimate and an adaptive mesh selection which enhances the efficiency of the code will be described in detail later. In this master thesis we present two classes of applications simulated using bvpsuite. The first application is a project in cooperation with the Department of Mathematics of the Palacky University in Olomouc, Czech Republic. It is concerned with the existence of solutions of nonlinear singular second order ordinary differential equation of the form u -- (t) =a/t - u - (t) + -f(t,u(t),u - (t)), t - (0,T), subject to periodic boundary conditions u(0) = u(T), u - (0) = u - (T). We illustrate this theory by means of numerical simulations. The second application is a simulation of a model for gas permeation, in cooperation with the Institute for Chemical Engineering of the Vienna University of Technology. It shows how using bvpsuite allows to handle difficult models which cannot be treated effectively using standard techniques.