Approximation methods for the calculation of eigenvalues in ODE with periodic or anti periodic boundary conditions: Application to nanotubes

TL;DR

This paper compares three iterative methods for solving Sturm-Liouville problems with periodic or anti-periodic boundary conditions, demonstrating their efficiency through tests on the Mathieu equation and applying them to model carbon nanotubes.

Contribution

It introduces a comparative analysis of three numerical methods for eigenvalue problems with specific boundary conditions, applied to nanotube modeling.

Findings

Successive approximation method shows competitive efficiency.

All methods effectively solve Mathieu equation eigenvalues.

Application to nanotubes demonstrates practical relevance.

Abstract

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.