Non linear wave propagation

(Difference between revisions)

Revision as of 23:28, 25 December 2005

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

$x \in \left[-5,10\right]$

$u(x,0) = \begin{cases} 0 & x \le 0 \\ 1 & x > 0 \end{cases}$

$u(0,t)=0$

$u(x,t) = \begin{cases} 0 & x \le 0 \\ x/t & 0 < x < t \\ 1 & \mbox{otherwise} \end{cases}$

@@ Line 2: / Line 2: @@
 :<math> \frac{\partial u}{\partial t}+ u \frac{\partial u}{\partial x}=0
 </math>
 == Domain ==
-x=[-5,10]
+:<math>x \in \left[-5,10\right]</math>
 == Initial Condition ==
-:<math> u(x,0)=0 ,x <=0 </math>
+:<math>u(x,0) =
-:<math> u(x,0)=1 ,x >0  </math>
+\begin{cases}
+& x \le 0 \\
+& x > 0
+\end{cases}
+</math>
 == Boundary condition ==
-u[0]=0
+:<math>u(0,t)=0</math>
 == Exact solution ==
-:<math> u(x,t)=0 ,x<=0 </math>
+:<math>u(x,t) =
-:<math> u(x,t)=x/t, 0<x<t </math>
+\begin{cases}
-:<math> u(x,t)=1.0 ,\mbox{otherwise} </math>
+& x \le 0 \\
+x/t & 0 < x < t \\
+& \mbox{otherwise}
+\end{cases}
+</math>
 == Numerical method ==
 == Results ==
 [[Image:Nonlinear_1d.png]]
 == Reference ==