# Non linear wave propagation

(Difference between revisions)
 Revision as of 17:59, 22 December 2005 (view source)← Older edit Revision as of 01:43, 25 December 2005 (view source)Newer edit → Line 1: Line 1: == Problem definition == == Problem definition == - + :$\frac{\partial u}{\partial t}+ c \frac{\partial u}{\partial x}=0 - == Domain and grid == +$ - + == Domain == + x=[0,1] == Initial Condition == == Initial Condition == + :$u(x,0)=e^{-360*{(x-0.25)}^2}$ == Boundary condition == == 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 == == Numerical method == + c=1,t=0.25 + == Results == + [[Image:Linear_1d.jpg]] - == Results == + == Reference ==

## Problem definition

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

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

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

c=1,t=0.25