I need help with this MATLAB code to achive this picture:

xmin $=0$;

xmax $=1$;

N $=100$;

dt $=0\mathrm{.}009$;

t $=0\mathrm{.}3$;

tmax $=0\mathrm{.}5$;

v $=1$;

dx $=($xmax $-$ xmin$)/$N;

x $=$ xmin $-$ dx : dx : xmax $+$ dx;

if x $<mtext></mtext><mn>1</mn>$;

u$0=$ exp$(-(1/(1-($x$^2))))$;

else

u$0=0$;

u $=$ u$0$;

unp$1=$ u$0$;

nsteps $=$ tmax$/$dt;

for n $=1$ : nsteps

u$(1)=$ u$(3)$;

u$($N$+3)=$ u$($N$+1)$;

for i $=2$ : N $+2$

unp$1($i$)=$ u$($i$)-$ vdt$/$dx$($u$($i$)-$ u$($i$-1))$;

end

t $=$ t $+$ dt;

u $=$ unp$1$;

exact $=$ exp$(-200($x$-0\mathrm{.}25-$vt$).^2)$;

plot$($x$,$exact, $\text{'}$r$-\text{'})$;

hold on

plot$($x$,$u$,\text{'}$bo$-\text{'},$ 'markerfacecolor' $,\text{'}$b$\text{'})$;

hold off

axis $([$xmin xmax $-0\mathrm{.}51\mathrm{.}5])$

xlabel$(\text{'}$x$\text{'},$'fontsize',$16)$

ylabel$(\text{'}$U$($t$,$x$)\text{'},$'fontsize',$16)$

title$($sprintf$(\text{'}$time $=\%1\mathrm{.}3$f$\text{'},$t$),$'fontsize',$16)$

shg

pause$($dt$)$;

end

$($c$)$ Modify your initial code $($forward upwind $=$ forward in time $+$ backward in space$)$ so

that the domain is $-1,1.$ Take Plot your solution at time

$t=0\mathrm{.}3$ and $t=0\mathrm{.}5.$ Save your plots as PNG files.