What is it about?

The approach proposed in the paper completes rigorous proofs of the existence and localisation of zeros of broad families trigonometric and cylindrical polynomials. The choice of initial approximation is validated which enables one to perform substantiated calculations of zeros and justify thus iterative numerical solution techniques. The method is applied to the determination of roots of dispersion equations in electromagnetics and acoustics.

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Why is it important?

Our findings show how one can organize and justify analytical and numerical procedures to determine zeros of trigonometric and cylindrical polynomials and to apply the results for the analysis of various resonance and wave phenomena in electromagnetics.

Perspectives

The approach can be generalized to wider polynomial families and explain the occurrence of roots, real or complex, of dispersion equations that describe waves and resonant frequencies. The method can be incorporated to commercial solvers and textbooks and monographs in field theory. In fact, it reveals the nature of resonances by providing better understanding of the mathematical origin of the existence of roots of dispersion equations.

Yury Shestopalov
University of Gävle

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This page is a summary of: Trigonometric and cylindrical polynomials and their applications in electromagnetics, Applicable Analysis, February 2019, Taylor & Francis, DOI: 10.1080/00036811.2019.1584290.
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