Solution Using Jacobi and Gauss Seidel Method.

Question

Pranjal Pathak 2012-1-23

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https://ww2.mathworks.cn/matlabcentral/answers/26828-solution-using-jacobi-and-gauss-seidel-method

回答： Meysam Mahooti 2019-11-29

Hi,

I am facing problem regarding the solution of the foll problem:

W(m+1)(j,k)=Pm(j,k)+Q(j,k)/2*g(j,k) Where: P(j,k)=[W(j+1,k)+W(j-1,k)+W(j,k+1)+W(j,k-1)]/g(j,k) Q(j,k)=Sy(j,k+1)- Sy(j,k-1)+ Sx(j+1,k)-Sy(j-1,k) m=m-th iterations(say 4) g(j,k)={2, if j=1:N or k=1:N 3, if j=1:N or k=2:N-1, k=1:N or j=2:N-1 4 otherwise} N=128

             Sx=sqrt(8).*(9.*X.^3+3.*Y.^2-2)
             Sy=sqrt(8).*(6.*X.*Y)
And [X,Y] =meshgrid(-1:2/127:+1,-1:2/127:+1)               
Which will give us the Q-matrix
The initial W-matrix is assumed to be a zero matrix having all the elements zero(128x128).

Can anyone help me in solving this problem using 1] Jacobi Method, and 2] Gauss Seidel Method upto a iteration of 4 in MATLAB.