Non linear wave propagation

(Difference between revisions)

Revision as of 01:48, 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[imax]=u[imax-1](x[imax]=1.0)

$u(x,t)=e^{-360*{((x-c*t)-0.25)}^2}$

c=1,t=0.25

@@ Line 1: / Line 1: @@
 == Problem definition ==
-:<math> \frac{\partial u}{\partial t}+ c \frac{\partial u}{\partial x}=0
+:<math> \frac{\partial u}{\partial t}+ u \frac{\partial u}{\partial x}=0
 </math>
 == Domain ==
-x=[0,1]
+x=[-5,10]
 == Initial Condition ==
-:<math> u(x,0)=e^{-360*{(x-0.25)}^2}</math>
+:<math> u(x,0)=0 ,x <=0 </math>
+:<math> u(x,0)=1 ,x >0  </math>
 == Boundary condition ==
 u[0]=0,u[imax]=u[imax-1](x[imax]=1.0)
@@ Line 15: / Line 15: @@
 c=1,t=0.25
 == Results ==
-[[Image:Linear_1d.jpg]]
+[[Image:Nonlinear_1d.jpg]]
 == Reference ==