# Non linear wave propagation

(Difference between revisions)
 Revision as of 01:43, 25 December 2005 (view source)← Older edit Revision as of 01:48, 25 December 2005 (view source)Newer edit → Line 1: Line 1: == Problem definition == == Problem definition == - :$\frac{\partial u}{\partial t}+ c \frac{\partial u}{\partial x}=0 + :[itex] \frac{\partial u}{\partial t}+ u \frac{\partial u}{\partial x}=0$ [/itex] == Domain == == Domain == - x=[0,1] + x=[-5,10] == Initial Condition == == Initial Condition == - :$u(x,0)=e^{-360*{(x-0.25)}^2}$ + :$u(x,0)=0 ,x <=0$ - + :$u(x,0)=1 ,x >0$ == Boundary condition == == Boundary condition == u[0]=0,u[imax]=u[imax-1](x[imax]=1.0) u[0]=0,u[imax]=u[imax-1](x[imax]=1.0) Line 15: Line 15: c=1,t=0.25 c=1,t=0.25 == Results == == Results == - [[Image:Linear_1d.jpg]] + [[Image:Nonlinear_1d.jpg]] == Reference == == Reference ==

## Problem definition

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

x=[-5,10]

## Initial Condition

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

## Boundary condition

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

## Exact solution

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

c=1,t=0.25