The vibrating inhomogeneous string: a topic for a course in Computational Physics

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.