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The spectrum and the stability of the Chebyshev collocation operator for transonic flow

Author: Dalia Fishelov
Journal: Math. Comp. 51 (1988), 559-579
MSC: Primary 65M10; Secondary 76H05
MathSciNet review: 930225
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Abstract: The extension of spectral methods to the small disturbance equation of transonic flow is considered. It is shown that the real parts of the eigenvalues of its spatial operator are nonpositive. Two schemes are considered; the first is spectral in the x and y variables, while the second is spectral in x and of second order in y. Stability for the second scheme is proved. Similar results hold for the two-dimensional heat equation.

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Keywords: Spectral methods, transonic flow, stability, Chebyshev polynomials, eigenvalue problems
Article copyright: © Copyright 1988 American Mathematical Society

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