UDC 519.6
EFFICIENT TWO-SIDED ESTIMATES FOR THE SPECTRUM OF SOME
ELLIPTIC OPERATORS
Abstract. Using the minimax principle, we establish the upper and lower bounds for the spectrum of some elliptic operators and their grid analogs. From the exact formulas for the error of the finite-difference method for the eigenvalues, more accurate estimates of the spectrum of differential operators follow. Two-sided estimates of the eigenvalues of differences analogs of spectral problems give a majorant and a minorant for the error of the phase velocities of grid waves in vibration problems of various objects.
Keywords: elliptic operators, minimax principle, finite-difference method, exact formulas for errors of eigenvalues, two-sided estimates of a spectrum, oscillation equations, errors of phase velocities of grid waves.
FULL TEXT
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