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Convergence of Gauss Seidel Iterative Method

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Old   September 19, 2017, 15:49
Default Convergence of Gauss Seidel Iterative Method
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Karan Anand
Join Date: May 2017
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Hello everyone,

I am developing a code in FORTRAN to solve 2d steady state heat conduction equation(Laplace equation) problem using Gauss Seidel iterative method.
Right now I am running the solution upto 1000 iterations and getting a solution.
However, I want the solution to stop iterating as soon as it converges.
I am using a three dimensional array to store the values of temparature. The main code snippet for gauss seidel iterations is given below.(k: iterations, i: x nodes, j: y nodes):

Code:
DO K = 2, 1000
  DO I = 2, 39
    DO J = 2, 19
       T(K, I, J) = 0.25*(T(K, I-1, J) + T(K-1, I+1, J) + T(K, I, J-1) + T(K-1, I, J+1))
    END DO
  END DO
END DO
Please suggest how can I stop this as the solution converges.
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