consider the first order wave equation for a unit step function moving at a speed c$=1$m$/$s in a domain extending from x$=0$ to $1$m

$1.$slove the first order wave equation using the first order explicit method.plot the finite difference solution and the analytics solution on the same cooradiante system.explain the difference.

$2.$how long does it take for a wave to travelthe distance from x$=0($left boundary$)$ to x$=1$m$?$ show a detailed calculation