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Non linear wave propagation

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== Problem definition ==
== Problem definition ==
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:<math> \frac{\partial u}{\partial t}+ c \frac{\partial u}{\partial x}=0
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== Domain and grid ==  
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</math>
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== Domain ==  
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x=[0,1]
== Initial Condition ==  
== Initial Condition ==  
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:<math> u(x,0)=e^{-360*{(x-0.25)}^2}</math>
== Boundary condition ==  
== Boundary condition ==  
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u[0]=0,u[imax]=u[imax-1](x[imax]=1.0)
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== Exact solution ==
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:<math> u(x,t)=e^{-360*{((x-c*t)-0.25)}^2}</math>
== Numerical method ==  
== Numerical method ==  
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c=1,t=0.25
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== Results ==
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[[Image:Linear_1d.jpg]]
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== Results ==
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== Reference ==

Revision as of 01:43, 25 December 2005

Contents

Problem definition

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

Domain

x=[0,1]

Initial Condition

 u(x,0)=e^{-360*{(x-0.25)}^2}

Boundary condition

u[0]=0,u[imax]=u[imax-1](x[imax]=1.0)

Exact solution

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

Numerical method

c=1,t=0.25

Results

Linear 1d.jpg

Reference

My wiki