Analytical and numerical investigation of the spectra of three-point difference operators |
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Authors: | L V Dorodnitsyn |
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Institution: | (1) Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia |
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Abstract: | The properties of the spectra of discrete spatially one-dimensional problems of convection — diffusion type with constant
coefficients and nonstandard boundary conditions are examined in the framework of stability of explicit algorithms for time-dependent
problems of mathematical physics. An analytical method is proposed for finding isolated limit points of the operator spectrum.
Limit points are determined for the difference transport equation with different versions of nonreflecting boundary conditions
and for an approximation of the heat conduction equation on a grid with condensation near the boundary. Stability and other
properties of the spectrum are also established numerically.
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Translated from Prikladnaya Matematika i Informatika, No. 27, pp. 25–45, 2007. |
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