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

DOI:
https://doi.org/10.1090/S0025-5718-1988-0930225-0

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0930225-0

Keywords:
Spectral methods,
transonic flow,
stability,
Chebyshev polynomials,
eigenvalue problems

Article copyright:
© Copyright 1988
American Mathematical Society