Non linear wave propagation

(Difference between revisions)

Revision as of 01:51, 25 December 2005

$\frac{\partial u}{\partial t}+ u \frac{\partial u}{\partial x}=0$

x=[-5,10]

$u(x,0)=0 ,x <=0$

$u(x,0)=1 ,x >0$

u[0]=0

$u(x,t)=0 ,x<=0$

$u(x,t)=x/t, 0<x<t$

$u(x,t)=1.0 ,\mbox{otherwise}$

@@ Line 11: / Line 11: @@
 == Exact solution ==
-:<math> u(x,t)=e^{-360*{((x-c*t)-0.25)}^2}</math>
+:<math> u(x,t)=0 ,x<=0 </math>
+:<math> u(x,t)=x/t, 0<x<t </math>
+:<math> u(x,t)=1.0 ,\mbox{otherwise} </math>
 == Numerical method ==
-c=1,t=0.25
 == Results ==
 [[Image:Nonlinear_1d.jpg]]
 == Reference ==