The spectrum and the stability of the Chebyshev collocation operator for transonic flow
Abstract
The extension of spectral methods to the smalldisturbance 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 twodimensional heat equation.
 Publication:

Mathematics of Computation
 Pub Date:
 October 1988
 Bibcode:
 1988MaCom..51..559F
 Keywords:

 Chebyshev Approximation;
 Computational Fluid Dynamics;
 Finite Difference Theory;
 Numerical Stability;
 Small Perturbation Flow;
 Spectral Methods;
 Transonic Flow;
 Asymptotic Properties;
 Differential Equations;
 Eigenvalues;
 Fourier Transformation;
 Mach Number;
 Fluid Mechanics and Heat Transfer