Approximation methods for the calculation of eigenvalues in ODE with periodic or anti periodic boundary conditions: Application to nanotubes
Incremental comparison of known numerical methods for a specific class of ODEs, with limited practical impact.
The paper compares three methods for solving Sturm-Liouville problems with periodic/antiperiodic boundary conditions, using the Mathieu equation as a test case. The methods are applied to a carbon nanotube model, but no concrete performance numbers are reported.
We compare three different methods to obtain solutions of Sturm-Liouville problems: a successive approximation method and two other iterative methods. We look for solutions with periodic or anti periodic boundary conditions. With some numerical test over the Mathieu equation, we compare the efficiency of these three methods. As an application, we make a numerical analysis on a model for carbon nanotubes.