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A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE’s

Published online by Cambridge University Press:  03 June 2015

Kosuke Abe ,
Nobuyuki Higashimori ,
Masayoshi Kubo ,
Hiroshi Fujiwara  and
Yuusuke Iso
Kosuke Abe*
Affiliation:
Nihon University, Tokyo, Japan
Nobuyuki Higashimori*
Affiliation:
Hitotsubashi University, Kunitachi, Japan
Masayoshi Kubo*
Affiliation:
Graduate School of Informatics, Kyoto University, Kyoto, Japan
Hiroshi Fujiwara*
Affiliation:
Graduate School of Informatics, Kyoto University, Kyoto, Japan
Yuusuke Iso*
Affiliation:
Graduate School of Informatics, Kyoto University, Kyoto, Japan
*
Email: k-abe@penta.ge.cst.nihon-u.ac.jp
Email: higashim@econ.hit-u.ac.jp
Email: kubo@i.kyoto-u.ac.jp
Email: fujiwara@acs.i.kyoto-u.ac.jp
Corresponding author. Email: iso@acs.i.kyoto-u.ac.jp
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Abstract

The Courant-Friedrichs-Lewy condition (The CFL condition) is appeared in the analysis of the finite difference method applied to linear hyperbolic partial differential equations. We give a remark on the CFL condition from a view point of stability, and we give some numerical experiments which show instability of numerical solutions even under the CFL condition. We give a mathematical model for rounding errors in order to explain the instability.

Keywords

65M0665M1265G50Numerical analysisfinite difference schemestabilityCFL condition
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 5 , October 2014 , pp. 693 - 698
Copyright
Copyright © Global-Science Press 2014

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References

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