Gaussian spectral rules for second order finite-difference schemes

Numerical Algorithms

Volumn 25, Issue 1-4, 2000, Pages 139-159

  Druskin, Vladimir ^a   Knizhnerman, Leonid ^b  

^a SCHLUMBERGER DOLL RESEARCH   (United States)

^b Central Geophysical Expedition   (Russian Federation)

Author keywords

Elliptic and hyperbolic problems; Exponential superconvergence; Finite differences; Nyquist limit; Pad Chebyshev approximant

Indexed keywords

EID: 0000279344     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1016600805438     Document Type: Article

References (15)

1. S. Asvadurov, V. Druskin and L. Knizhnerman, Application of the difference Gaussian rules to solution of hyperbolic problems, J. Comput. Phys. 158 (2000) 116-135.
2. G.A. Baker and P. Graves-Morris, Padé Approximants (Addison-Wesley, London, 1996).
3. L. Berlyand and K. Golden, Exact result for the effective conductivity of a continuum percolation model, Phys. Rev. B 50(4) (1994) 2114-2117.
4. V. Druskin and L. Knizhnerman, Padé, Stieltjes, Lanczos and exponential superconvergence of finite-difference schemes, in: Proc. of Copper Mountain Conf. on Iterative Methods, Vol. II, March-April 1998.
5. V. Druskin and L. Knizhnerman, Gaussian spectral rules for the three-point second differences: I. A two-point positive definite problem in a semiinfinite domain, SIAM J. Numer. Anal. 37 (1999) 403-422.
6. B. Fornberg, Practical Guide to Pseudospectral Methods (Cambridge Univ. Press, Cambridge, 1996).
7. G. Freud, Orthogonal Polynomials (Pergamon, Oxford, 1976).
8. D.V. Ingerman, Personal communication, Courant Institute, New York (December 1997).
9. D. Ingerman, V. Druskin and L. Knizhnerman, Optimal finite-difference grids and rational approximations of the square root. I. Elliptic problems, Comm. Pure Appl. Math. 53(8) (2000) 1039-1066.
10. I.S. Kac and M.G. Krein, On the spectral functions of the string, Amer. Math. Soc. Transl. 103 (1974) 19-102.
11. S. Moskow, Personal communication, Ridgefield (December 1997).
12. O. Nevanlinna, Convergence of Iterations for Linear Equations, Lectures in Mathematics (Birkhäuser, ETH Zürich, 1993).
13. S.A. Orzag, Spectral methods for problems in complex geometries, J. Comput. Phys. 37 (1980) 70-92.
14. B. Strand, Simulations of acoustic wave phenomena using high-order finite difference approximations, SIAM J. Sci. Comput. 20(5) (1999) 1585-1604.
15. R.S. Varga, Matrix Iterative Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1962).