Numerical evidence of Kneser solutions and convergence of collocation applied to singular ODEs

Abstract

In the first chapter of the work, we give numerical evidence of Kneser solutions for second order ordinary differential equations with a singularity of the first kind on a semi infinite intervall. The main goal is to illustrate the existence theory of Kneser solutions and their asymptotic behavior In the second part of the work, we test the convergence properties of the collocation schemes applied to solve a system of linear ordinary differential equations with a singularity of the first kind.