Prikazchikov V.
Efficient two-sided estimates for the spectrum of some elliptic operators

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. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: elliptic operators, error of phase velocities of grid waves, exact formulas for errors of eigenvalues, finite-difference method, maximum principle, oscillation equations, two-sided estimates of spectrum, Eigenvalues and eigenfunctions, Finite difference method, Mathematical operators, Maximum principle, Phase velocity, Eigen-value, Elliptic operator, Error of phase velocity of grid wave, Exact formula for error of eigenvalue, Exact formulas, Finite-difference methods, Oscillation equation, Spectra's, Two-sided estimate of spectrum, Upper and lower bounds, Errors

Cite:
Prikazchikov V. (2022). Efficient two-sided estimates for the spectrum of some elliptic operators. Cybernetics and Systems Analysis, 58 (3), 111-122. doi: https://doi.org/10.1007/s10559-022-00481-y http://jnas.nbuv.gov.ua/article/UJRN-0001323862 [In Ukrainian].