The errors in calculating the pseudospectral differentiation matrices for Čebyšev-Gauss-Lobatto points

Computers and Mathematics with Applications

Volumn 37, Issue 1, 1999, Pages 41-48

  Baltensperger, R ^a   Berrut, J P ^a  

^a UNIVERSITY OF FRIBOURG   (Switzerland)

Author keywords

Barycentric formula; eby ev points; Differentiation matrix; Roundoff error; Spectral methods

Indexed keywords

DIFFERENTIATION (CALCULUS); ERROR ANALYSIS; MATRIX ALGEBRA; PROBLEM SOLVING;

CEBYSEV-GAUSS-LOBATTO POINTS; DIFFERENTIATION MATRIX; ROUNDOFF ERRORS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0032761614     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00240-5     Document Type: Article

References (12)

1. J.P. Boyd, Chebyshev and Fourier Spectral Methods, Springer Verlag, Berlin, (1989).
2. P. Canuto, M.Y. Hussaini, A. Quarteroni and T. Zang, Spectral Methods in Fluid Dynamics, Springer, New York, (1988).
3. B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, (1996).
4. D. Funaro, A preconditioning matrix for the Chebyshev differencing operator, SIAM J. Numer. Anal. 24, 1024-1031 (1987).
5. D. Funaro, Computing the inverse of the Chebyshev collocation derivative, SIAM J. Sci. Stat. Comput. 9, 1050-1057 (1988).
6. L.N. Trefethen and M.R. Trummer, An instability phenomenon in spectral methods, SIAM J. Numer. Anal. 24, 1008-1023 (1987).
7. T. Tang and M.R. Trummer, Boundary layer resolving pseudospectral methods for singular perturbation problems, SIAM J. Sci. Comput. 17, 430-438 (1996).
8. S.C. Reddy and L.N. Trefethen, Stability of the method of lines, Numer. Math. 62, 235-267 (1992).
9. K.S. Breuer and R.M. Everson, On the errors incurred calculating derivatives using Chebyshev polynomials, J. Comput. Phys. 99, 56-67 (1992).
10. R. Peyret, Introduction to Spectral Methods, von Karman Institute Lecture Series, Rhode-St-Genese, (1986).
11. B.D. Welfert, A remark on pseudospectral differentiation matrices, Department of Mathematics, Arizona State University, Tempe, AZ, (1992).
12. B.D. Welfert, Generation of pseudospectral differentiation matrices I, SIAM J. Numer. Anal. 34, 1640-1657 (1997).