Index exceeds the number of array elements. Index must not exceed 2.

I am tryin to solve Laplace's equation using the finite difference method using the code below I get the following error, "Index exceeds the number of array elements. Index must not exceed 2.". Any help on how to combat this error would be much appreciated.

function u = Laplace_annular(r1,r2)

% Specifying parameters
Sec = 40; % Number of section iterations
Ang = 100; % Number of angle iterations
dtheta= 2*pi/Ang; % Number of angle steps (radians)
dr = (r1 - r2)/Ang;
r = r1:dr:r2;
theta = 0:dtheta:2*pi;
[r,theta] = meshgrid(r,theta);

% Initialising solution array
u = zeros(Ang+1,Sec+1);
u_0 = zeros(Ang+1,Sec+1);
u(1,:) = u(1,:)+1;
u(2,:) = u(2,:)+0;

% Solving equation
beta = dr^2/dtheta^2;
n = 1;
k = 0;
while k == 0
    u_0 = u;
    k = 1;
    for i = 2:80
        for j = 2:40
            r(j) = 1 + (j-1)*dr;
            theta(i) = dtheta/2 + (i-1)*dtheta;
            ua1 = ((r(j) + r(j+1))/2)*u_0(i,j+1) + ((r(j)+r(j-1))/2)*u_0(i,j-1);
            ua2 = beta*u_0(i+1,j) + beta*u_0(i-1,j);
            ua = ua1 + ua2;
            ub = ((r(j)+r(j+1))/2)+((r(j)+r(j-1))/2)+2*beta;
            u(i,j) = ua/ub;
            if abs(u(i,j)-u_0(i,j))>(10^-5)
                k=0;
            end
        end
    end
    n=n+1;
end

end

Answer 1

[Torsten]

dr = (r1 - r2)/Ang;

implies r1 > r2

r = r1:dr:r2;

implies r2 > r1

So what is correct ?

[Joshua Ustaran-Anderegg]

I see. It should be r1 > r2

[Torsten]

Then you know what you have to do ?

r = r2:dr:r1

instead of

r = r1:dr:r2;

And most probably you mean

dr = (r1 - r2)/Sec;

instead of

dr = (r1 - r2)/Ang;

?

And in the looping part

for i = 2:100

instead of

for i = 2:80    

?

[Joshua Ustaran-Anderegg]

Thank you very much