Laplace solved by Gauss-Seidel

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Kornelija Paulauskaite 2017-12-6

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/371473-laplace-solved-by-gauss-seidel

The code delivers the same answer for any choice of NX or NY. There's a problem somewhere but I cannot find it..

NX=100; NY=100; Lx=5; Ly=5; x=linspace(0,Lx,NX); y=linspace(0,Ly,NY); u=zeros(NX,NY); u1=0; u2=900; u3=0; u4=0; err=1; k=0; tic; while max(err(:))>0 k=k+1;

    uold=u;
for i=2:NX-1
    for j=2:NY-1
        u(i,j)=.25*(u(i+1,j)+u(i+1,j)+u(i,j+1)+u(i,j-1));
        u(:,NX)=u1; 
        u(:,1)=u2;
        u(1,:)=u3;
        u(NY,:)=u4;
        unew=u;
        err=abs((uold-unew)./unew);
    end
end
end
toc;
for i=1:NX
    for j=1:NY
        n=i+(j-1)*NX;
        ui(i,j)=u(n);
    end
end
surf(x,y,ui')
fprintf('number of iterations is :%f',k)
timetaken=toc