Symbolic Investigation of the Spectral Characteristics of Guided Modes in Smoothly Irregular Waveguides

This paper considers a homogeneous system of functional equations that occurs when solving a spectral problem the eigenfunctions of which describe guided modes of smoothly irregular waveguides. The resulting system of functional equations is a homogeneous system of algebraic equations for any fixed...

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Bibliographic Details
Published in:Programming and computer software 2022-04, Vol.48 (2), p.80-89
Main Authors: Divakov, D. V., Tyutyunnik, A. A.
Format: Article
Language:English
Subjects:
Approximation
Artificial Intelligence
Boundary conditions
Computer algebra
Computer Science
Eigenvectors
Functional equations
Investigations
Mathematical analysis
Numerical analysis
Numerical methods
Operating Systems
Regularization methods
Software Engineering
Software Engineering/Programming and Operating Systems
Variables
Waveguides
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Summary:This paper considers a homogeneous system of functional equations that occurs when solving a spectral problem the eigenfunctions of which describe guided modes of smoothly irregular waveguides. The resulting system of functional equations is a homogeneous system of algebraic equations for any fixed argument. A symbolic method for solving systems of functional equations of this type is proposed. The method is implemented in the Maple computer algebra system. Results of numerical computations are presented to demonstrate the effectiveness of the developed symbolic-numerical method in comparison with the approach based on only numerical techniques.
ISSN:0361-7688
1608-3261
DOI:10.1134/S0361768822020049