Question $1$

Solve for $p$ at times $0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}6,0\mathrm{.}8$ and $1$ given

$\frac{\text{d}\text{e}\text{l}\text{p}}{\text{d}\text{e}\text{l}\text{t}}=p,=0\mathrm{.}8$

$IC$: $p(t=0)=18$

In solving the above problem, use the explicit, implicit and Crank Nicholson schemes and

compare your results with the exact solution $($analytical solution$).$ Use a timestep size $(t)$

of $0\mathrm{.}2$