Parse error at '=' and ')' in FEM approach

Hi,

Following is my code and it is related to FEM.

T = zeros(10,5);
T(1:10,1) = 10;
T(1:10,5) = 50;
T(1,2) = 73;
T(1,3) = 100;
T(1,4) = 85;

for n=1:9
    for i =2:4
        (1/6)*0.1*(T(n+1,i-1)-(T(n,i-1)))+(2/3)*0.1*(T(n+1,i)-T(n,i))+(1/6)*0.1*(T(n+1,i+1)-T(n,i+1)) = 2*(T(n,i+1)-2*T(n,i)+T(n,i-1));
    end  
end

I'm getting the following errors.

"Parse error at '=': usage might be invalid MATLAB syntax" (Line 10)

"Parse error at ')': usage might be invalid MATLAB syntax" (Line 10)

This is my first attempt in this kind of mathematical approach and I'm sure the code is pretty primary, to say the least. However, Can anyone tell me what should I try to fix this?

TIA!

[Geoff Hayes]

James - what is your intent with the line of code

(1/6)*0.1*(T(n+1,i-1)-(T(n,i-1)))+(2/3)*0.1*(T(n+1,i)-T(n,i))+(1/6)*0.1*(T(n+1,i+1)-T(n,i+1)) = 2*(T(n,i+1)-2*T(n,i)+T(n,i-1));

? What are you trying to calculate? You have equations on both sides of the equals sign which will lead to the (in this case) syntax errors. Please discuss what you are attempting to do.

[Jake]

Of course.

Here, I'm trying to work with Finite Element Method. The equation that I'm using is as follows.

I need to find the converged solution for the equation, assuming dT =0.1 and (alpha/dx)=2. I'm not sure whether my approach is correct though but I'm following the same question and solution discussed in here.https://www.mathworks.com/matlabcentral/answers/516366-finite-difference-method-to-find-steady-state

I note that the equation is faulty because I have multiplied the terms by 0.1 instead of dividing the terms.But I don't think that was the reason for the aforementioned error.

[Geoff Hayes]

A problem is the left-hand sign of your equation - you are not assigning the right-hand side to something on the left-hand side since it (the left) is an equation in its own right. Consider the answer from the link you posted

T(n+1,i) = T(n,i) + 0.3*(T(n,i+1)-2*T(n,i)+T(n,i-1));

You will (somehow) need to formulate your new equation like this one where an equation/calculation on the right is assigned to an array element on the left. Or perhaps for FEM (which I have no experience) there is an alternative workflow that you can follow.

[Jake]

That does make sense. I will try to find more help with FEM in matlab here as well.

Thank you, Geoff!