$1.$ Use a for loop to create a matrix called psiold that has vertical values spanning from $0$ to $16$ for

every column.

$2.$ Create a zeroes matrix called psinew that is the same size as psiold.

$3.$ Create a variable called tol that represents the tolerance limit at which the while loop will stop.

Set tol equal to $0\mathrm{.}001.$

$4.$ Create a variable called counter to track how many while loop iterations are done before the

tolerance is satisfied. Set counter equal to $0.$

$5.$ Create a while loop that runs as long as there are any points at which abs$($psinew$-$psiold$)>$tol are

not satisfied. Remember that abs$($psinew$-$psiold$)>$tol is a logical expression that will returns $1$s or

$0$s depending on if the condition is satisfied or not. The while condition should have the logical

expression nested into another logical expression to account for there being any points where the

first logical expression is still true.

$6.$ Nested within the while loop, created a nested for loop that evaluates psinewi,j as the average of

the four surrounding psiold points. See equation below:

$,=(+1,+,+1+1,+,1)/4$

Note that the boundary rows and columns need to be excluded from the nested for loop,

otherwise the expression will be trying to reference index values outside of psiold. The boundary

conditions will be addressed below.

$7.$ Create a second for loop, still nested within the while loop, that defines the first column of psinew

as values spanning from $0$ to $16.$ This should be the same as you did in step $1$ with the exception

that you are only doing it for the first columns, rather than all columns.

$8.$ Define the last column of psinew as the same as the second to last column of psinew. This is still

nested within the while loop.

$9.$ Define the first row of psinew as equal to $0.$ This is still nested within the while loop.

$10.$ Define the last row of psinew as equal to $16.$ This is still nested within the while loop.

$11.$ Define rows $1$ through $9$ and columns $21$ through $29$ of psinew as equal to zero. This is to account

for the area of no flow, as described in the previous figure.

$12.$ Create an if statement, still nested within the while loop, that does the same logical check as was

created in step $5$ to see if there are any points where the tolerance is not satisfied. If the condition

is true, define psiold as psinew and define psinew as all zeros.

$13.$ Increment the counter by $1$ and end the while loop.

$14.$ Display the counter.

$15.$ Create a contour plot of psinew, with $16$ streamlines.

$16.$ Set the axis equal and label and title the contour plot.

$17.$ What happens to the counter value as the tolerance is increased and decreased?