could you please help me with this topic about gauss seidle

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

[Walter Roberson]

I am not clear what the difference is between this and https://www.mathworks.com/matlabcentral/answers/845360-how-do-i-use-contour-command-for-rectangular-plate?s_tid=srchtitle ?

[mehmet salihi]

Both give same results.

Point Gauss gives the converge solution in 574 iteration (above code)

whereas, Line Gauss gives in 308 iteration (under developing)

Line gausse method has diagonal matrix, it is implicit method. and we have more than 1 unknown. and it is converge fast than point Guass method.

the code ı shared above is for Point Gauss, but i could not find the idea how to reshape for 5-16 formula.

the grid points above is illustrates the method for Lıne Gauss and for the point Guass method the below is applied.

i am developing 5-16 formulation.