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Non linear wave propagation

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:<math> u(x,0)=1 ,x >0  </math>   
:<math> u(x,0)=1 ,x >0  </math>   
== Boundary condition ==  
== Boundary condition ==  
-
u[0]=0,u[imax]=u[imax-1](x[imax]=1.0)
+
u[0]=0
== Exact solution ==
== Exact solution ==

Revision as of 01:49, 25 December 2005

Contents

Problem definition

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

Domain

x=[-5,10]

Initial Condition

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

Boundary condition

u[0]=0

Exact solution

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

Numerical method

c=1,t=0.25

Results

Nonlinear 1d.jpg

Reference

My wiki