Superconvergence of the Shortley-Weller approximation for Dirichlet problems

Journal of Computational and Applied Mathematics

Volumn 116, Issue 2, 2000, Pages 263-273

  Matsunaga, Nami ^a   Yamamoto, Tetsuro ^a  

^a EHIME UNIVERSITY   (Japan)

Author keywords

Dirichlet problems* Shortley Weller formula; Finite difference methods; Superconvergence

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; PROBLEM SOLVING;

DIRICHLET PROBLEMS; HOLDER EXPONENT; SHORTLEY-WELLER APPROXIMATION; SUPERCONVERGENCE;

APPROXIMATION THEORY;

EID: 0033876599     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00321-0     Document Type: Article

References (13)

1. Bramble J.H., Hubbard B.E. On the formulation of finite difference analogues of the Dirichlet problem for Poisson's equation. Numer. Math. 4:1962;313-327.
2. X. Chen, N. Matsunaga, T. Yamamoto, Smoothing Newton methods for nonsmooth Dirichlet problems, in: M. Fukushima, L. Qi (Eds.), Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer, Dordrecht, 1998, pp. 65-79.
3. R. Courant, D. Hilbert, Methods of Mathematical Physics, Vol. 2, Interscience, New York, 1962.
4. G.E. Forsythe, W.R. Wasaw, Finite Difference Methods for Partial Differential Equations, Wiley, New York, 1960.
5. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977.
6. W. Hackbusch, Elliptic Differential Equations, Springer, Berlin, 1992.
7. J.M. Ortega, Numerical Analysis, A Second Course, Academic Press, New York, 1972.
8. G.I. Marchuk, V.V. Shaidurov, Difference Methods and their Extrapolations, Springer, Berlin, 1983.
9. Matsunaga N. Comparison of three finite difference approximations for Dirichlet problems. Information. 2:1999;55-64.
10. J.C. Strikwerda, Y. Nagel, Finite difference methods for polar coordinate systems, MRC Technical Summary Report #2934, University of Wisconsin-Madison, 1986.
11. R.S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962.
12. D.M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York, 1971.
13. T. Yamamoto, On the accuracy of finite difference solution for Dirichlet problems, RIMS Kokyuroku No. 1040, Study of Numerical Algorithms, Kyoto University, 1998, pp. 135-142.