MATLAB Program for Successive Over-Relaxation (SOR)

MATLAB Programs:

% SOR (Successive Over-Relaxation)

 n = input('Enter number of equations, n:  ');

 A = zeros(n,n+1);

 x1 = zeros(1,n);

 A=[4 2 3 8; 3 -5 2 -14; -2 3 8 27];

 x1 = [0 0 0];

 tol = input('Enter tolerance, tol:  ');

 m = input('Enter maximum number of iterations, m:  ');

 w = input('Enter the parameter w (omega):  ');

 k = 1;

 while  k <= m

   err = 0;

   for i = 1 : n

      s = 0;

      for j = 1 : n

        s = s-A(i,j)*x1(j);

      end

      s = w*(s+A(i,n+1))/A(i,i);

      if abs(s) > err

         err = abs(s);

      end

      x1(i) = x1(i)+s;

   end

  

   if err <= tol 

      break;

   else

      k = k+1;

   end

 end

 fprintf('The solution vector after %d iterations is :\n', k);

 for i = 1 : n

 fprintf('   %11.8f \n', x1(i));

 end

OUTPUTs:
>> successive_over_relaxation
Enter number of equations, n:  3
Enter tolerance, tol:  0.001
Enter maximum number of iterations, m:  50
Enter the parameter w (omega):  1.25
The solution vector after 29 iterations is :
   -1.00019013 
    2.99962341 
    2.00017040 
>>