Spectral analysis of hermite cubic spline collocation systems

SIAM Journal on Numerical Analysis

Volumn 36, Issue 6, 1999, Pages 1962-1975

  Sun, Weiwei ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Differentiation matrices; Eigenvalues; Spline collocation

Indexed keywords

EID: 0001601728     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997322722     Document Type: Article

References (24)

1. M. B. ALLEN AND G. F. PINDER, Collocation simulation of multiphase porous-medium flow, J. Society of Petroleum Engineers, Feb. (1983), pp. 135-142.
2. U. M. ASCHER, J. CHRISTIANSEN, AND R. D. RUSSELL, Collocation software for boundary-value ODEs, ACM Trans. Math. Software, 7 (1981), pp. 209-222.
3. U. ASCHER AND G. BADER, Stability of collocation at Gaussian points, SIAM J. Numer. Anal., 23 (1986), pp. 412-422.
4. U. M. ASCHER, R. M. MATTHEIJ, AND R. D. RUSSELL, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1988.
5. B. BIALECKI, G. FAIRWEATHER, AND K. R. BENNETT, Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations, SIAM J. Numer. Anal., 29 (1992), pp. 156-173.
6. C. CANUTO, M. Y. HUSSAINI, A. QUARTERONI, AND T. A. ZANG, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, 1988.
7. J. H. CERUTTI AND S.V. PARTER, Collocation methods for parabolic partial differential equations in one space dimension, Numer. Math., 26 (1976), pp. 227-254.
8. C. DE BOOR AND B. SWARTZ, Collocation at Gaussian points, SIAM J. Numer. Anal., 10 (1973), pp. 582-606.
9. W. R. DYKSEN, Tensor product generalized ADI methods for separable elliptic problems, SIAM J. Numer. Anal., 24 (1987), pp. 59-76.
10. W. R. DYKSEN, R. E. LYNCH, J. R. RICE, AND E. N. HOUSTIS, The performance of the collocation and Galerkin methods with Hermite bicubics, SIAM J. Numer. Anal., 22 (1984), pp. 695-715.
11. W. HUANG AND D. SLOAN, A new pseudospectral method with upwind features, IMA J. Numer. Anal., 13 (1993), pp. 413-430.
12. D. GOTTLIEB AND E. LUSTMAN, The spectrum of the Chebyshev collocation operator for the heat equation, SIAM J. Numer. Anal., 20 (1983), pp. 909-921.
13. D. MAHMOOD AND M. R. OSBORNE, Collocation for BVPs: Compact and noncompact schemes, in Computational Techniques and Applications: CTAC93, D. Stewart, H. Gardner, and D. Singleton, eds., World Scientific, River Edge, NJ, pp. 354-361, 1994.
14. A. R. MITCHELL AND D. F. GRIFFITHS, The Finite Difference Method in Partial Differential Equations, John Wiley & Sons, Chichester, 1980.
15. G. F. PINDER AND A. SHAPIRO, A new collocation method for the solution of the convection-dominated transport equation, Water Resources Research, 15 (1979), pp. 1177-1182.
16. P. M. PRENTER AND R. D. RUSSELL, Orthogonal collocation for elliptic partial differential equations, SIAM J. Numer. Anal., 13 (1976), pp. 923-939.
17. J. R. RICE AND R. F. BOISVERT, Solving Elliptic Problems Using Ellpack, Springer-Verlag, New York, 1985.
18. C. RINGHOFER, On collocation schemes for quasilinear singularly perturbed boundary value problems, SIAM J. Numer. Anal., 21 (1984), pp. 864-882.
19. R. D. RUSSELL AND W. SUN, Spline collocation differentiation matrices, SIAM J. Numer. Anal., 34 (1997), pp. 2274-2287.
20. A. M. SHAPIRO AND G. F. PINDER, Analysis of an upstream weighted collocation approximation to the transport equation, J. Comput. Phys., 39 (1981), pp. 46-71.
21. W. SUN AND N. G. ZAMANI, A fast algorithm for solving the tensor product collocation equations, J. Franklin Inst., 326 (1989), pp. 295-307.
22. W. SUN, Iterative algorithms for orthogonal spline collocation linear systems, SIAM J. Sci. Comput., 16 (1995), pp. 720-737.
23. W. SUN, A high-order direct method for solving Poisson's equation on a disc, Numer. Math., 70 (1995), pp. 501-506.
24. J. A. C. WEIDEMAN AND L. N. TREFETHEN, The eigenvalues of second-order spectral differentiation matrices, SIAM J. Numer. Anal., 25 (1988), pp. 1279-1295.