Attempted to access U(2,0); index must be a positive integer or logical.

here is my Guass-seidal program for poisson equation, how will i overcome this error.

function U=Guassseidal(n,m,a,b,c,d,tol,N)
n=3; %input('enter the value of n=  ');
m=3; %input('enter the value of m=  ');
a=0; % input('enter the value of a=  ');
b=3; %input('enter the value of b=  ');
c=0; %input('enter the value of c=  ');
d=3; %input('enter the value of d=  ');
tol=0.001; %input('enter the value of tolerance=  ');
N=2; %input('enter the total number of iterations =  ');
A=-10; %input('input F(x,y)::::if your fuction is variable use inline('') ');  
Bc1=0;%input('enter the Boundary condition at U(x,c) ');
Bc2=0;%input('enter the Boundary condition at U(x,d) ');
Bc3=0;%input('enter the Boundary condition at U(a,y) ');
Bc4=0;%input('enter the Boundary condition at U(b,y) ');
h=(b-a)/n;
k=(d-c)/m;

for i=1:n-1
for j=1:m-1
    x(i)=a+i*h;
    y(i)=c+j*k;
end
end
for i=1:n-1
for j=1:m-1
    U(i,j)=0;
end
end
for i=2:n-1
        U(i,c)=Bc1;
        U(i,d)=Bc2;
 for j=1:m
            U(a,j)=Bc3;
            U(b,j)=Bc4;
end
end

        alpha=2*(1+h^2/k^2);
        K=1;
        while K<=N 
            errchk=0;
         for j=2:m-3
                for i=2:n-3
                    S=((-h^2)*A+U(i-1,j)+U(i+1,j)+(0.5*alpha-1)*(U(i,j-1)+U(i,j+1)))/alpha;
                    if errchk<abs(S-U(i,j))
                        errchk=abs(S-U(i,j));
                        U(i,j)=S;
                        if errchk<=tol
                        end
                            for j=1:m-1
                                for i=1:n-1
     disp(U)                           
     disp('succesfully complete with solution ')
     
                        end
                    end
                end
         end
    K=K+1;
        end
        disp('number of iterations exceed, unsuccessful completion')
        end
        
end

        

     
    

[Stephen23]

What is the point in carefully defining eight input arguments that you completely ignore?

[Zuhaa Naz]

actually firstly i want my program to be like that user input these eight arguments by himself, but then i moved to a specfic example. so i ignored them

[Adam]

Use the debugger to find where your code is passing a 0 to U as an index and change it so you no longer do it. As the error message very coherently says, indices must be positive integers or logicals. 0 is neither.

[Zuhaa Naz]

i have changed the indices from i-1 to i, and then further changes... I have also started loop from i=2 instead of i=1, but unfortunately it moves outside the grid....

[Walter Roberson]

When you do this kind of work, in any case in which you subtract something from your index, then the index must start 1 higher than the maximum that you subtract, so that after the subtraction the lowest value would be 1.

Likewise in any case in which you add something to an index, then the index must stop by that much lower than the maximum, so that after the addition you do not exceed the maximum.

It is sometimes necessary to have additional code to deal with the boundary conditions.

[Zuhaa Naz]

Yes you are absolutely right. Will you please tell me which additional code is used to deal with boundary conditions

[Walter Roberson]

I am not familiar enough with the mathematics to say what the boundary conditions should be. But it probably involves the Bc* variables.