Index in position 1 is invalid- attempting to perform Laplace's equation

I've been trying to use Laplace's equation to model the temperature gradient in the cross section of two tubes, here's the code:

[X,Y,T] = meshgrid(0:0.1:10, 0:0.1:10, zeros);
for k = 1:1000
    for i = 1:100
        for j = 1:100
            if ((0.1*i)-6)^2 + ((0.1*j)-5)^2 <= 6.25
                T(i,j) = 100;
            end
            if ((0.1*i)-5)^2 + ((0.1*j)-5)^2 <= 25
                T(i,j) = 0;
            end
            T(i,j) = 0.25*(T((0.1*i)-1,(0.1*j))+T((0.1*i)+1,(0.1*j))+T((0.1*i),(0.1*j)-1)+T((0.1*i),(0.1*j)+1));
        end
    end
end
surf(X,Y,T)

Everything works fine before I insert line 11, and when I do, I get the error message

"Index in position 1 is invalid. Array indicies must be positive integers or logical values".

For the record, I've tried doing it without multiplying all the variables in the equation by 0.1, that was just one of my many attempts to get this to work.

What am I doing wrong, and what should I do to fix it?

[Setsuna Yuuki.]

do you have the math function you tested in code?

[Tethys Robertson]

Yes, I'm trying to use it as a relaxation method at line 11.

To make it less convoluted:

T(i,j) = 0.25(T(i-1,j)+T(i+1,j)+T(i,j-1)+T(i,j+1))

[VBBV]

 [X,Y] = meshgrid(0:0.1:10, 0:0.1:10);
 T = zeros(size(X));

    for i = 2:length(X)
        for j = 2:length(Y)-1
            if ((0.1*i)-6)^2 + ((0.1*j)-5)^2 <= 6.25
                T(i,j) = 100;
            end
            if ((0.1*i)-5)^2 + ((0.1*j)-5)^2 <= 25
                T(i,j) = 0;
            else
            T(i,j) = 0.25*(T(i-1,j)*0.1+T(i,j)*0.1+T(i,j-1)*0.1+T(i,j+1)*0.1); % you might want this
            end
        end
    end
surf(X,Y,T)

Try the above

[Tethys Robertson]

Thanks, the program actually runs now, but when it does the smoothing looks odd and unprogressed- here are some photos for reference:

What might it be that I'm doing wrong?

[Tethys Robertson]

Here's a view from the top (note that I also removed the parts multiplying each variable by 0.1)

[Tethys Robertson]

Actually, I just noticed that there was a missing "+1" next to the "i" in the second term of the equation, but now I'm getting an error that says "Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters", highlighting the semicolon. This is the code I'm using:

T(i,j) = 0.25*(T((i-1),j)+T((i+1),j)+T(i,(j-1))+T(i,(j+1));

EDIT: never mind, I found the missing bracket and fixed that, but now I'm getting whatever this is:

Answer 1

[Alan Stevens]

In your loops, 0.1i and 0.1j will result in non integer values for most values of i and j. Indices in T(i,j) etc must be integers (>=1), so T(0.1*i-1,0.1j) could have indices that are non-integer (and even negative), so are inadmissable.