Program does not show the matrix

This program is made to approximate the solution to the Poisson equation. I have no errors with the equations, but it won't display the matrix and proceeds with displaying "End". Please help

a=0;
b=2;
c=0;
d=1;
m=5;
n=6;
N= 100;
TOL = 10^-4;

syms ga(y) gb(y) gc(x) gd(x) f(x,y);
f(x,y)=x*exp(y);
ga(y)=0;  
gb(y)=2*exp(y);  
gc(x)=x;                     
gd(x) =x*exp(1);   

h=(b-a)/n;
k=(d-c)/m;

for i = 1:n-1
    xi(i)=a+i*h;   
end

for j = 1:m-1
    yj(j)=c+j*k;
end

for i=1:n-1
    for j=1:m-1
        wij(i,j)=0;
    end
end

lambda=h^2/k^2;
mu=2*(1+lambda);
l=1;

while l <= N
    
    z=(-(h^2)*f(xi(1),yj(m-1))+ga(yj(m-1))+lambda*gd(xi(1))+lambda*wij(1,m-2)+wij(2,m-1))/mu;
    NORM=abs(z-wij(1,m-1));
    wij(1,m-1)=z;
    
    for i=2:n-2
        z = (-h^2*f(xi(i),yj(m-1))+lambda*gd(xi(i))+wij(i-1,m-1)+wij(i+1,m-1)+lambda*wij(i,m-2))/mu;
        if abs(wij(i,m-1)-z)>NORM
            NORM = abs(wij(i,m-1)-z);
        end
        wij(i,m-1) = z;
    end
    
    z=(-h^2*f(xi(n-1),yj(m-1))+gb(yj(m-1))+lambda*gd(xi(n-1))+wij(n-2,m-1)+lambda*wij(n-1,m-2))/mu;
    if abs (wij(n-1,m-1)-z) > NORM 
        NORM = abs (wij(n-1,m-1)-z);
    end
    wij(n-1,m-1)=z;
    
    for j=m-2:-1:2
        
        z=(-(h^2)*f(xi(1),yj(j))+ga(yj(j))+lambda*wij(1,j+1)+lambda*wij(1,j-1)+wij(2,j))/mu;
        if abs(wij(1,j)-z)>NORM
            NORM = abs(wij(1,j)-z);
        end
        wij(i,j)=z;
        
        for i=2:n-2
            z=(-(h^2)*f(xi(i),yj(j))+wij(i-1,j)+lambda*wij(i,j+1)+wij(i+1,j)+lambda*wij(i,j-1))/mu;
            if abs (wij(i,j)-z)>NORM
                NORM=abs(wij(i,j)-z);
            end
            wij(i,j)=z;
        end

        z=(-h^2*f(xi(n-1),yj(j))+gb(yj(j))+wij(n-2,j)+lambda*wij(n-1,j+1)+lambda*wij(n-1,j-1))/mu;
        if abs(wij(n-1,j)-z)>NORM
            NORM=abs(wij(n-1,j)-z);
        end
        wij(n-1,j)=z;
    end
    
    z = (-h^2*f(xi(1),yj(1))+ga(yj(1))+lambda*gc(xi(1))+lambda*wij(1,2)+wij(2,1))/mu;
    if abs(wij(1,1)-z) > NORM
        NORM = abs(wij(1,1)-z);
    end
    wij(1,1) = z;

    for i = 2:n-2
        z = (-h^2*f(xi(i),yj(1))+lambda*gc(xi(i))+wij(i-1,1)+lambda*wij(i,2)+wij(i+1,1))/mu;
        if abs(wij(i,1)-z)>NORM
            NORM = abs(wij(i,1)-z);
        end
        wij(i,1) = z;
    end

    z=(-h^2*f(xi(n-1),yj(1))+gb(yj(1))+lambda*gc(xi(n-1))+wij(n-2,1)+lambda*wij(n-1,2))/mu;
        if abs (wij(n-1,1)-z) > NORM
            NORM= abs(wij(n-1,1)-z) ;
        end
        wij(n-1,1)=z;

    if NORM<= TOL 

        for i=1:n-1
            for j=1:m-1
                MATRIX(i)=[xi(i) yj(j) wij(i,j)];
            end
        end
        display(MATRIX)
    end
    l=l+1;    
end
display("End")

[Rik]

I restored the edit from Google cache.

@LightFury Yeji it is very rude to edit away major parts of your question after receiving an answer. Please don't do it again.

[LightFury Yeji]

Hi! Sorry for that, I did it because the answer is not correct and I thought it would confuse others. I would not do it again.

Answer 1

[Walter Roberson]

a=0;
b=2;
c=0;
d=1;
m=5;
n=6;
N= 100;
TOL = 10^-4;

syms ga(y) gb(y) gc(x) gd(x) f(x,y);
f(x,y)=x*exp(y);
ga(y)=0;  
gb(y)=2*exp(y);  
gc(x)=x;                     
gd(x) =x*exp(1);   

h=(b-a)/n;
k=(d-c)/m;

for i = 1:n-1
    xi(i)=a+i*h;   
end

for j = 1:m-1
    yj(j)=c+j*k;
end

for i=1:n-1
    for j=1:m-1
        wij(i,j)=0;
    end
end

lambda=h^2/k^2;
mu=2*(1+lambda);
l=1;

found = 0;
while l <= N
    if found > 0
        fprintf('solution was already found at iteration #%d, why did we start iteration %#d\n', found, l);
    end
    z=(-(h^2)*f(xi(1),yj(m-1))+ga(yj(m-1))+lambda*gd(xi(1))+lambda*wij(1,m-2)+wij(2,m-1))/mu;
    NORM=abs(z-wij(1,m-1));
    wij(1,m-1)=z;
    
    for i=2:n-2
        z = (-h^2*f(xi(i),yj(m-1))+lambda*gd(xi(i))+wij(i-1,m-1)+wij(i+1,m-1)+lambda*wij(i,m-2))/mu;
        if abs(wij(i,m-1)-z)>NORM
            NORM = abs(wij(i,m-1)-z);
        end
        wij(i,m-1) = z;
    end
    
    z=(-h^2*f(xi(n-1),yj(m-1))+gb(yj(m-1))+lambda*gd(xi(n-1))+wij(n-2,m-1)+lambda*wij(n-1,m-2))/mu;
    if abs (wij(n-1,m-1)-z) > NORM 
        NORM = abs (wij(n-1,m-1)-z);
    end
    wij(n-1,m-1)=z;
    
    for j=m-2:-1:2
        
        z=(-(h^2)*f(xi(1),yj(j))+ga(yj(j))+lambda*wij(1,j+1)+lambda*wij(1,j-1)+wij(2,j))/mu;
        if abs(wij(1,j)-z)>NORM
            NORM = abs(wij(1,j)-z);
        end
        wij(i,j)=z;
        
        for i=2:n-2
            z=(-(h^2)*f(xi(i),yj(j))+wij(i-1,j)+lambda*wij(i,j+1)+wij(i+1,j)+lambda*wij(i,j-1))/mu;
            if abs (wij(i,j)-z)>NORM
                NORM=abs(wij(i,j)-z);
            end
            wij(i,j)=z;
        end

        z=(-h^2*f(xi(n-1),yj(j))+gb(yj(j))+wij(n-2,j)+lambda*wij(n-1,j+1)+lambda*wij(n-1,j-1))/mu;
        if abs(wij(n-1,j)-z)>NORM
            NORM=abs(wij(n-1,j)-z);
        end
        wij(n-1,j)=z;
    end
    
    z = (-h^2*f(xi(1),yj(1))+ga(yj(1))+lambda*gc(xi(1))+lambda*wij(1,2)+wij(2,1))/mu;
    if abs(wij(1,1)-z) > NORM
        NORM = abs(wij(1,1)-z);
    end
    wij(1,1) = z;

    for i = 2:n-2
        z = (-h^2*f(xi(i),yj(1))+lambda*gc(xi(i))+wij(i-1,1)+lambda*wij(i,2)+wij(i+1,1))/mu;
        if abs(wij(i,1)-z)>NORM
            NORM = abs(wij(i,1)-z);
        end
        wij(i,1) = z;
    end

    z=(-h^2*f(xi(n-1),yj(1))+gb(yj(1))+lambda*gc(xi(n-1))+wij(n-2,1)+lambda*wij(n-1,2))/mu;
        if abs (wij(n-1,1)-z) > NORM
            NORM= abs(wij(n-1,1)-z) ;
        end
        wij(n-1,1)=z;

    if NORM<= TOL 

        for i=1:n-1
            for j=1:m-1
                MATRIX(i)=[xi(i) yj(j) wij(i,j)];
            end
        end
        display(MATRIX)
        found = l;
    end
    l=l+1;    
end
display("End")

    "End"

if found == 0
    fprintf('Solution was never found, ran out of iterations\n');
else
    fprintf('Solution was found at iteration #%d\n', found);
end

Solution was never found, ran out of iterations

[LightFury Yeji]

I'm sorry, this program has an expected output -- solution should be found.