Krylov subspace spectral methods for variable-coefficient initial-boundary value problems

Electronic Transactions on Numerical Analysis

Volumn 20, Issue , 2005, Pages 212-234

  Lambers, James V ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Gaussian quadrature; Lanczos method; Spectral methods; Variable coefficient

Indexed keywords

EID: 29344432412     PISSN: 10689613     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. J. P. BOYD, Chebyshev and Fourier Spectral Methods, 2nd edition, Dover Publications, Inc., Mineola, NY, 2001.
2. D. CALVETTI, G. H. GOLUB, W. B. GRAGG, AND L. REICHEL, Computation of Gauss-Kronrod quadrature rules, Math. Comp., 69 (2000), pp. 1035-1052.
3. G. H. GOLUB AND C. MEURANT, Matrices, Moments and Quadrature, in Proceedings of the 15th Dundee Conference, June-July 1993, D. F. Griffiths and G. A. Watson (eds.), Longman Scientific & Technical, 1994.
4. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd edition, Johns Hopkins University Press, 1996.
5. J. GOODMAN, T. Hou, AND E. TADMOR, On the stability of the unsmoothed Fourier method for hyperbolic equations, Numer. Math., 67 (1994), pp. 93-129.
6. P. GUIDOTTI, J. V. LAMBERS, AND K. SØLNA, Analysis of Wave Propagation in ID Inhomogeneous Media, to appear in Numer. Funct. Anal. Optim., 2005.
7. B. GUSTAFSSON.H.-O. KREISS, AND J. OLIGER, Time-Dependent Problems and Difference Methods, Wiley, New York, 1995.
8. M. HOCHBRUCK AND C. LUBICH, On Krylov Subspace Approximations to the Matrix Exponential Operator, SIAM J. Numer. Anal., 34 (1996), pp. 1911-1925.
9. C. JOHNSON, Numerical solutions of partial differential equations by the finite element mehod, Cambridge University Press, 1987.
10. J. V. LAMBERS, Krylov Subspace Methods for Variable-Coefficient Initial-Boundary Value Problems, Ph.D. Thesis, Stanford University, SCCM Program, 2003, available at http://sccm.stanford.edu/pub/sccm/theses/ James_Lambers.pdf.
11. _, Approximating Eigenfunctions of Variable-Coefficient Differential Operators, in preparation.
12. _, Practical Implementation of Krylov Subspace Spectral Methods, submitted.
13. _, A Stability Analysis of Krylov Subspace Spectral Methods, in preparation.
14. P. E. SAYLOR AND D. C. SMOLARSKI, Why Gaussian quadrature in the complex plane?, Numer. Algorithms, 26 (2001), pp. 251-280.
15. J. STOER AND R. BURLISCH, Introduction to Numerical Analysis, 2nd edition, Springer-Verlag, 1983.