The stability of pseudospectral-Chebyshev methods
Math. Comp. 36 (1981), 107-118
Primary 65N30; Secondary 65N35
Full-text PDF Free Access
Similar Articles |
Abstract: The stability of pseudospectral-Chebyshev methods is demonstrated for parabolic and hyperbolic problems with variable coefficients. The choice of collocation points is discussed. Numerical examples are given for the case of variable coefficient hyperbolic equations.
Gottlieb and Steven
A. Orszag, Numerical analysis of spectral methods: theory and
applications, Society for Industrial and Applied Mathematics,
Philadelphia, Pa., 1977. CBMS-NSF Regional Conference Series in Applied
Mathematics, No. 26. MR 0520152
H. O. Kreiss & J. Oliger, Methods for the Approximate Solution of Time Dependent Problems, G.A.R.P. Publication Series, No. 10, 1973.
Gottlieb and Eli
Turkel, On time discretizations for spectral methods, Stud.
Appl. Math. 63 (1980), no. 1, 67–86. MR 578457
Gunzburger, and Eli
Turkel, On numerical boundary treatment of hyperbolic systems for
finite difference and finite element methods, SIAM J. Numer. Anal.
19 (1982), no. 4, 671–682. MR 664877
J. Rivlin, The Chebyshev polynomials, Wiley-Interscience [John
Wiley & Sons], New York, 1974. Pure and Applied Mathematics. MR 0450850
- D. Gottlieb & S. A. Orszag, Numerical Analysis of Spectral Methods, Theory and Applications, NSF-CBMS Monograph No. 26, SIAM, Philadelphia, Pa., 1977. MR 0520152 (58:24983)
- H. O. Kreiss & J. Oliger, Methods for the Approximate Solution of Time Dependent Problems, G.A.R.P. Publication Series, No. 10, 1973.
- D. Gottlieb & E. Turkel, "On time discretizations for spectral methods," ICASE Report 78-1; Studies in Applied Math. (To appear.) MR 578457 (82j:65083)
- D. Gottlieb, M. Gunzburger & E. Turkel, "On numerical boundary treatment for hyperbolic systems," ICASE Report 78-13; SIAM J. Numer. Anal. (To appear.) MR 664877 (83f:65154)
- T. J. Rivlin, The Chebyshev Polynomials, Wiley, New York, 1974. MR 0450850 (56:9142)
Retrieve articles in Mathematics of Computation
Retrieve articles in all journals
© Copyright 1981 American Mathematical Society