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Volume 6, Issue 5
A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE's

Kosuke Abe, Nobuyuki Higashimori, Masayoshi Kubo, Hiroshi Fujiwara & Yuusuke Iso

DOI: 10.4208/aamm.2014.5.s6

Adv. Appl. Math. Mech., 6 (2014), pp. 693-698.

Published online: 2014-06

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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

Numerical analysis, finite difference scheme, stability, CFL condition.

  • AMS Subject Headings

65M06, 65M12, 65G50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-693, author = {Abe , KosukeHigashimori , NobuyukiKubo , MasayoshiFujiwara , Hiroshi and Iso , Yuusuke}, title = {A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE's}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {5}, pages = {693--698}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.5.s6}, url = {http://global-sci.org/intro/article_detail/aamm/43.html} }
TY - JOUR T1 - A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE's AU - Abe , Kosuke AU - Higashimori , Nobuyuki AU - Kubo , Masayoshi AU - Fujiwara , Hiroshi AU - Iso , Yuusuke JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 693 EP - 698 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2014.5.s6 UR - https://global-sci.org/intro/article_detail/aamm/43.html KW - Numerical analysis, finite difference scheme, stability, CFL condition. AB -

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.

Abe , KosukeHigashimori , NobuyukiKubo , MasayoshiFujiwara , Hiroshi and Iso , Yuusuke. (2014). A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE's. Advances in Applied Mathematics and Mechanics. 6 (5). 693-698. doi:10.4208/aamm.2014.5.s6
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