How to solve a system of two linear equations in matrix form under a loop /

Suppose that I have two coordinates, time and space , and two dependent variables c and T such that and . Now I have a system of two coupled equations which are given in matrices form as

I define the t and x vectors in the code as follows. How to calculate the matrix X inside the loops given below. Initial data is available, i.e. and are given.

 for j=1:50
    
 t(j)=j*0.05; % t vector
   
 end
 
 for i=1:50
    
 x(i)=i*0.05; % space vector
   
 end
 
 %___________________________ running the loop_______________________________________


for j=1:50 
    
for i=1:50
       
 %???????? How to calculate the matric X here ????????????????????
 
 
end

end

[Jon]

Is this a typo?

 x(i)=i*0.05; % space vector

Did you mean

  c(i)=i*0.05; % space vector

[Adnan Hayat]

No, it is not a typo. Actually i define x and t vectors like that. YOu can ignore that and take x=1,2,3,...,50 and t=1,2,3,...,50

Answer 1

[Jon]

I'll assume you know how to calculate A and B based upon your c and T values. Then to solve for X use

X = M\(J*A + B)

Note that using the \ operator is more numerically robust and efficient than actually computing the matrix inverse of M

[Adnan Hayat]

The problem is how to store the value of M\(J*A + B) in X?

[Jon]

You could store the results in a 3 dimensional array, so

X = zeros(2,50,50); % preallocate
    for i = 1:50
        for j = 1:50
            .
            .
            .
            X(:,i,j) = M\(J*A + B)
            
        end
    end