could you please help me with this topic about gauss seidle

Question

mehmet salihi 2021-6-2

0
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https://ww2.mathworks.cn/matlabcentral/answers/846455-could-you-please-help-me-with-this-topic-about-gauss-seidle

编辑： mehmet salihi 2021-6-2

i can do PGS method with the below code > equation 5-15, code is below

iam trying to develop it to LGS method > equation 5-16, please need your help. the logic forf interior points are attached also.

the number of iteration have to be 308

any other information needed, will be shared.

example solution,

%%% Point Gauss Seidel (PGS) 
clear
close all, clc
format short g
%Defining the constants
L=1;                                % length
H=2;                                % Height
deltax=0.05
deltay=0.05
Beta=deltax/deltay
Beta2=Beta^2
jn=H/deltay                         % Maximum number of grid points along y
im=L/deltax                         % Maximum number of grid points along x
T1=100; T2=0; T3=0; T4=0;           % boundary conditions
y=2:-deltay:0;
x=0:deltax:L;
% initialize T_old to the initial guess values
T_old=zeros(jn+1,im+1);
% set boundary conditions
T_old(1,1:im+1)=T1;
T_old(jn+1,1:im+1)=T3;
T_old(2:jn+1,1)=T2;
T_old(2:jn+1,im+1)=T4;
T_new = T_old;
Error = 0.011;  % could be any number that is greater than Errormax
Errormax=0.01;
t=0;
while Error > Errormax
    t=t+1;
    for i=2:jn 
        for j=2:im
            T_new(i,j)=(1/(2*(1+Beta2)))* (T_new(i-1,j)+T_new(i+1,j)+Beta2*(T_new(i,j+1)+T_new(i,j-1)) ) ;       
        end
    end
Error = sum(sum(abs(T_old-T_new),2))   ; 
T_old = T_new;
end
% create contour plot
contour(x,fliplr(y),T_new,17,'k')
xlabel('X')
ylabel('Y')
axis equal