Create A and B arrays given number of elements N and boundary temperature values

Create a MATLAB function of the form

[A,b] = makecoeff(N,Tleft,Tright)

That creates the A and b arrays given the number of elements N and the boundary temperature values. Report the results for N = 3.

Temperature of Tleft = 5 and Tright = 115.

Where the equation is Tn = (N/L)^2((Tn-1 - Tn) + (Tn+1 - Tn))

Where n = 1:N

Answer 1

[Vaibhav]

Hi Stephanie

You can follow the below steps to build the funtion.

Initialize the A matrix and b vector: You will need an N x N matrix A and an N x 1 vector b.

Set up the coefficients in matrix A:

• For the first row (i = 1), set the diagonal element to -2 and the element to the right to 1. The corresponding element in b should account for Tleft.
• For the last row (i = N), set the diagonal element to -2 and the element to the left to 1. The corresponding element in b should account for Tright.
• For the middle rows (2 ≤ i ≤ N-1), set the diagonal element to -2, the element to the left to 1, and the element to the right to 1.

Fill in the b vector:

• The first element in b should be -Tleft.
• The last element in b should be -Tright.
• The middle elements in b should be 0.

Display the results for specific values: If N = 3, Tleft = 5, and Tright = 115, display the A matrix and b vector to verify your results.

Here is a skeleton of the function to guide you:

function [A, b] = makecoeff(N, Tleft, Tright)
    % Initialize A matrix and b vector
    A = zeros(N, N);
    b = zeros(N, 1);
    
    % Fill the A matrix and b vector
    for i = 1:N
        if i == 1
            % Handle the first row
        elseif i == N
            % Handle the last row
        else
            % Handle the middle rows
        end
    end
    
    % Display results if N = 3
    if N == 3
        disp('A matrix:');
        disp(A);
        disp('b vector:');
        disp(b);
    end
end

Hope this helps!