View source for Courant number

A term used in the consideration of difference schemes for integrating one-dimensional hyperbolic systems. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026770/c0267701.png" /> is the grid spacing with respect to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026770/c0267702.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026770/c0267703.png" /> the grid spacing with respect to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026770/c0267704.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026770/c0267705.png" /> the maximum inclination of the characteristics, then the Courant number of the difference scheme equals <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026770/c0267706.png" />.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  S.K. Godunov,   V.S. Ryaben'kii,   "The theory of difference schemes" , North-Holland  (1964)  (Translated from Russian)</TD></TR></table>



====Comments====
The Courant number plays a role in the [[Courant–Friedrichs–Lewy condition|Courant–Friedrichs–Lewy condition]]. References are given there.