File:LF-Initial.png

Example of a discontinuous initial condition

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

applied to the illustration problem in the Lax–Friedrichs method article modified to have periodic boundary conditions; if ${\displaystyle a=1}$ 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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