File:LF-Initial.png

Summary

Example of a discontinuous initial condition

${\displaystyle u(x,0)=\{\begin{array}{cl}1& 0.4\le x\le 0.6\\ 0& \text{ otherwise }\end{array}}$

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

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

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