Abstract
The method of finite differences is one of fundamental techniques for solving boundary value problems of ordinary and partial differential equations, where ordinary and partial derivatives are replaced by divided differences.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bramble, J.H., Hubbard, B.E. (1962): On the formulation offinite difference analogues of the Dirichlet problem for Poisson’s equation. Numer. Math. 4: 313–327
Chen, X., Matsunaga, N., Yamamoto, T. (1999): Smoothing Newton methods for nonsmooth Dirichlet problems. In: Fukushima, M., Qi, L. (eds.): Reformulation—Nonsmooth, piecewise smooth, semismooth and smoothing methods. Kluwer, Dordrecht, pp. 65–79
Courant, R., Friedrichs, K.O., Lewy, H. (1928): Üeber die partiellen differenzengleichungen der mathematischen physik. Math. Annal. 100: 32–74 (English translation: (1967): On the partial difference equations of mathematical physics. IBM J. 11: 215–234)
Forsythe, G.E., Wasaw, W.R. (1960): Finite difference methods for partial differential equations. John Wiley & Sons, Inc., New York
Hackbusch, W. (1992): Elliptic differential equations. Springer Verlag, Berlin
Matsunaga, N. (1999): Comparison ofthree finite difference approximations for Dirichlet problems. Information 2: 55–64
Matsunaga, N., Yamamoto, T. (2000): Superconvergence of the Shortley-Weller approximation for Dirichlet problems. Journal Comp. Appl. Math. 116: 263–273
Strikwerda, J.C. (1989): Finite difference schemes and partial differential equations. Wadsworth, Inc., Belmont
Yamamoto, T. (1998): On the accuracy of finite difference solution for Dirichlet problems. In: RIMS Kokyuroku 1040, RIMS, Kyoto University, pp. 135–142
Yamamoto, T., Fang, Q., Chen, X. (2000): Superconvergence and nonsuperconvergence of the Shortley-Weller approximation for Dirichlet problems. (submitted)
Yamamoto, T., Ikebe, Y. (1979): Inversion of band matrix. Linear Algebra Appl. 24: 105–111
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Wien
About this paper
Cite this paper
Yamamoto, T. (2001). A New Insight of the Shortley-Weller Approximation for Dirichlet Problems. In: Alefeld, G., Rohn, J., Rump, S., Yamamoto, T. (eds) Symbolic Algebraic Methods and Verification Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6280-4_23
Download citation
DOI: https://doi.org/10.1007/978-3-7091-6280-4_23
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83593-7
Online ISBN: 978-3-7091-6280-4
eBook Packages: Springer Book Archive