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Linear wave propagation

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== Exact solution ==
== Exact solution ==
-
 
+
:<math> u(x,t)=e^{-360*{((x-c*t)-0.25)}^2}</math>
== Numerical method ==  
== Numerical method ==  
-
 
+
c=1,t=0.25
== Results ==
== Results ==
[[Image:Linear_1d.jpg]]
[[Image:Linear_1d.jpg]]
== Reference ==
== Reference ==

Revision as of 00:37, 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]

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