start-up flow poiseuille w/finite difference
 

hello,
I'd appreciate if someone with matlab knowledge could help me.
I'm trying to solve the above mentioned pde in matlab.

I have the following code:

clear;clc;
h = 1;
dr = 0.01; dt = 0.01;
nmax = 4000; epsilon = 0.0001;
r = [0:dr:h];
t = [0:dt:h];
beta=0.1;
n1 = fix(h/Dr)+1;
m1 = fix(h/Dt)+1;
% Initialize solution matrices
velocity = zeros(n1,m1)
velocityN =velocity
% Iterative process for the solution
for k = 1:nmax
% boundary conditions:
velocityN(:,n1) = zeros(n1,1);

% Calculate velocityN in interior points
for i = 2:n1-1
for j = 1:m1
velocityN(i,j+1)= (beta*(1-(1/(2*i)))*velocity(i-1,j)+(1-2*beta)*velocity(i,j)+beta*(1+1/(2*i))*velocity(i+1,j));
end;
end;
% Check convergence
nfail = 0;
for i = 1:n1
for j = 1:m1
if abs(velocityN(i,j)-velocity(i,j))>epsilon
nfail = nfail+1;
end;
end;
end;

if nfail > 0
velocity = velocityN;
else
return;
end;
end;
fprintf('No convergence after %i iterations.',k);
[X,Y] = meshgrid(r,t);
contour(X,Y,velocity',10)

however, for r=0 I have dv/dr=0 as the second boundary condition.

How do I incorporate this into the program.
dV/dr should be:
velocityN(0,j+1)=((1-4*beta)*velocity(0,j)+4*beta(velocity(1,j)))

Same with the initial condition say a constant 10 atm/cm is applied at t=0

thanks