ICASE/LaRC workshop on benchmark problems in computational aeroacoustics, category 1, problem 1

Solve the initial value problem

$\frac{\partial u}{\partial t} +\frac {\partial u}{\partial x} =0$
$u(x,0)=0.5 e^{-(ln 2) (\frac{x}{3}) ^2 }$

Computer the Numerical solution at t=100,200,300 and 400.

Exact Solution

$u(x,0)=0.5 e^{-(ln 2) (\frac{x -t }{3}) ^2 }$