Lax equivalence theorem

Lax equivalence theorem

In numerical analysis, the Lax equivalence theorem states a consistent finite difference approximation for a well-posed linear initial value problem is convergent if and only if it is stable. [Citation
last = Strikwerda
first = John C.
title = Finite Difference Schemes and Partial Differential Equations
edition = 1st
publisher = Chapman & Hall
year = 1989
pages = 26, 222]

This theorem is due to Peter Lax. It is sometimes called the Lax–Richtmyer theorem, after Peter Lax and Robert D. Richtmyer. [John Gary, "A Generalization of the Lax-Richtmyer Theorem on Finite Difference Schemes" SIAM Journal on Numerical Analysis, Vol. 3, No. 3 (Sep., 1966), pp. 467--473 [http://www.jstor.org/view/00361429/di976142/97p01105/0 JSTOR] ] [Richtmyer, Robert D.; Morton, K. W. "Difference methods for initial-value problems." Reprint of the second edition. Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1994. xiv+405 pp. ISBN 0-89464-763-6 [http://www.ams.org/mathscinet-getitem?mr=1275838 MR1275838] ] [Lax, P. D.; Richtmyer, R. D. Survey of the stability of linear finite difference equations. Comm. Pure Appl. Math. 9 (1956), 267--293 [http://www.ams.org/mathscinet-getitem?mr=79204 MR0079204] [http://dx.doi.org/10.1002/cpa.3160090206 doi:10.1002/cpa.3160090206] ]

References

External links

* [http://amsglossary.allenpress.com/glossary/search?id=lax-equivalence-theorem1 American Meteorological Society Glossary]
* [http://what.gi.alaska.edu/ao/sim/chapters/chap5.pdf Methods of Numerical Simulation, Chapter 5] p.62


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