Summary
In this note we discuss new, simple stability criteria for a wide class of finite difference approximations for initial-boundary value problems associated with the hyperbolic system ∂u/∂t = A∂u/∂x + Bu + f in the quarter plane x ⩾ 0, t ⩾ 0. With these criteria, stability is easily achieved for a multitude of examples that incorporate and generalize most of the cases studied in recent literature.
Research sponsored in part by U.S. Air Force Grants AFOSR-83-0150 and AFOSR-88-0175.
Research sponsored in part by NASA Contract NAS1-17070 and U.S.-Israel BSF Grant 85-00346.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Goldberg and E. Tadmor, Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II, Math. Comp. 36 (1981), 605–626.
M. Goldberg and E. Tadmor, Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems, Math. Comp. 44 (1985), 361–377.
M. Goldberg and E. Tadmor, Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems. II, Math. Comp. 48 (1987), 503–520.
B. Gustafsson, H.-O. Kreiss and A. Sundström, Stability theory of difference approximations for mixed initial boundary value problems. II, Math. Comp. 26 (1972), 649–686.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
About this chapter
Cite this chapter
Goldberg, M., Tadmor, E. (1989). Simple Stability Criteria for Difference Approximations of Hyperbolic Initial-Boundary Value Problems. In: Ballmann, J., Jeltsch, R. (eds) Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications. Notes on Numerical Fluid Mechanics, vol 24. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87869-4_18
Download citation
DOI: https://doi.org/10.1007/978-3-322-87869-4_18
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-528-08098-3
Online ISBN: 978-3-322-87869-4
eBook Packages: Springer Book Archive