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 - <p style="text-align: justify;">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.</p>