Second-order spectral differentiation matrices

SIAM Journal on Numerical Analysis

Volumn 33, Issue 6, 1996, Pages 2468-2487

  Sneddon, G E ^a  

^a JAMES COOK UNIVERSITY   (Australia)

Author keywords

Differentiation matrix; Eigenvalues; Polynomial interpolation; Spectral methods

Indexed keywords

EID: 1542785417     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994264237     Document Type: Article

References (15)

1. J. A. C. WEIDEMAN AND L. N. TREFETHEN, The eigenvalues of second-order spectral differentiation matrices, SIAM J. Numer. Anal., 25 (1988), pp. 1279-1298.
2. D. GOTTLIEB AND S. A. ORSZAG, Numerical Analysis of Spectral Methods: Theory and Applications, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1977.
3. C. CANUTO, M. Y. HUSSAINI, A. QUATERONI, AND T. ZANG, Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, 1988.
4. L. N. TREFETHEN AND M. R. TRUMMER, An instability phenomenon in spectral methods, SIAM J. Numer. Anal., 24 (1987), pp. 1008-1023.
5. D. R. GARDNER, S. A. TROGDON, AND R. W. DOUGLAS, A modified Tau spectral method that eliminates spurious eigenvalues, J. Comput. Phys., 80 (1989), pp. 137-167.
6. G. B. MCFADDEN, B. T. MURRAY, AND R. F. BOISVERT, Elimination of spurious eigenvalues in the Chebyshev Tau spectral method, J. Comput. Phys., 91 (1990), pp. 228-239.
7. W. HUANG AND D. M. SLOAN, The pseudospectral method for solving differential eigenvalue problems, J. Comput. Phys., 111 (1994), pp. 399-409.
8. D. GOTTLIEB AND E. TURKEL, On time discretization for spectral methods, Stud. Appl. Math., 63 (1980), pp. 67-86.
9. B. FORNBERG, An improved pseudospectral method for initial-boundary value problems, J. Comput. Phys., 91 (1990), pp. 381-397.
10. M. DUBINER, Asymptotic analysis of spectral methods, J. Sci. Comput., 2 (1987), pp. 3-31.
11. L. N. TREFETHEN AND J. A. C. WEIDEMAN, Two results on polynomial interpolation in equally, spaced points, J. Approx. Theory. 65 (1991), pp. 247-260.
12. W. S. DON AND D. GOTTLIEB, The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points, SIAM J. Numer. Anal., 31 (1994), pp. 1519-1534.
13. D. GOTTLIEB AND L. LUSTMAN, The spectrum of the spectral collocation operator for the heat equation, SIAM J. Numer. Anal., 20 (1983), pp. 909-921.
14. A. SOLOMONOFF AND E. TURKEL, Global properties of pseudospectral methods, J. Comput. Phys., 81 (1989), pp. 239-276.
15. M. ABRAMOWITZ AND I. STEGUN, Handbook of Mathematical Functions, Dover, New York, 1965.