The vibrating inhomogeneous string: a topic for a course in Computational Physics
Computational Physics
2010-06-11 v1 Mathematical Physics
math.MP
Abstract
This paper solves the integral equation which describes the oscillating inhomogeneous string, by using a spectral expansion method in terms of Chebyshev polynomials. The result is compared with the solution of the corresponding differential equation, obtained by expansion into a set of sine-wave functions, with emphasis on the accuracies of the two methods. These accuracies are determined by comparison with an iterative method which allows a precision of 1:10^11. The iterative method is based on a old method by Hartree, but contains innovative spectral expansion procedures.
Cite
@article{arxiv.1006.1913,
title = {The vibrating inhomogeneous string: a topic for a course in Computational Physics},
author = {George Rawitscher and Jakob Liss},
journal= {arXiv preprint arXiv:1006.1913},
year = {2010}
}
Comments
Accepted for publication in American Journal of Physics