Solving transcendental equations of physics with Chebyshev's method

Authors

DOI:

https://doi.org/10.55767/2451.6007.v34.n2.39487

Keywords:

Transcendental equations, Chebyshev, Mathematics, Physics, Root-finder

Abstract

In this work, physics teachers are provided with an optimized method to solve transcendental equations that cannot be solved algebraically and appear very often in higher education physics and engineering courses. The method is based on an interpolation with Chebyshev’s polynomials, and it is optimized for computational time, manageability, and accuracy. The method has been applied in specific problems of physics where transcendental equations appear, such as the compression of a real spring; the equation of a diode; the solution of the Schrödinger equation in a potential well; and the computing of cutoff wave numbers of a coaxial wire. The method is compared with others of the literature to check its correct behavior and the improvements that it presents. MATLAB source codes to implement the method and particular examples are also provided.

References

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Published

2022-11-29

Issue

Section

Essays and Special Topics

How to Cite

Solving transcendental equations of physics with Chebyshev’s method. (2022). Journal of Physics Teaching, 34(2), 97-108. https://doi.org/10.55767/2451.6007.v34.n2.39487