The spectral method is substantiated for the particular example of normal wave determination in a corrugated waveguide with rectangular-profile ribs. We establish the rib conditions, prove an analog of the Paley—Wiener theorem for Fourier series, and use the theorem to prove equivalence of the solutions of the original boundary-value problem and the dispersion equation. Some topics connected with the existence of the characteristic value of the dispersion equation and with the convergence of the approximate method are explored.
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Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 186–198, 1985.
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Il'inskii, A.S., Mutallimov, M.M. Spectral method in the theory of wave propagation in cellular periodic waveguides. Comput Math Model 1, 95–103 (1990). https://doi.org/10.1007/BF01128320
- Mathematical Modeling
- Wave Propagation
- Computational Mathematic
- Fourier Series
- Industrial Mathematic