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

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

2010-06-09

arxiv.org/abs/1006.1913v1

Physics

Computational Physics

Accepted for publication in American Journal of Physics

Scientific paper

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.

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