File:LF-Initial.png

Summary
Example of a discontinuous initial condition

$$u(x,0) = \left \{ \begin{array}{cl} 1 & 0.4 \leq x \leq 0.6 \\ 0 & \text{ otherwise } \end{array} \right . $$

applied to the illustration problem in the Lax–Friedrichs method article modified to have periodic boundary conditions; if $$a = 1$$ the exact solution at time $$t = 1$$ is identical to this initial condition.

Author: J. Steward Created using MATLAB v7.6.0.324 (R2008a)