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Efficient Two-Sided Estimates for the Spectrum of Some Elliptic Operators

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Cybernetics and Systems Analysis Aims and scope

Abstract

Using the principle of maximum, we establish the upper and lower bounds for the spectrum of some elliptic operators and their grid analogs. More accurate estimates of the spectrum of differential operators are obtained from the exact formulas for the error of the eigenvalues by the finite-difference method. Two-sided estimates of the eigenvalues of difference analogs of spectral problems give a majorant and a minorant for the error of the phase velocities of grid waves in vibration problems for various objects.

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    V. Prikazchikov

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  1. V. Prikazchikov
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Correspondence to V. Prikazchikov.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 3, May–June, 2022, pp. 111–122.

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Prikazchikov, V. Efficient Two-Sided Estimates for the Spectrum of Some Elliptic Operators. Cybern Syst Anal 58, 417–428 (2022). https://doi.org/10.1007/s10559-022-00481-y

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