MATLAB: Nested if statements not correctly calculating

finite differencesif statement

I'm solving a dirichlet problem using the upwind method and finite differences. I'm trying to construct the system of equations that I need so that I can obtain the coefficients and solve the system for the solution. Below is my code.. the output I get does not seem to include the i=2,j=2 case.. and I seem to be missing some variables as well. I am brand new to MATLAB, any help is appreciated.
clear
clc;
close all
%Step size and grid points
syms x y f u a
h=0.25;
k=0.05;
xv=1:h:9;
yv=1:k:4;
n=length(xv);
m=length(yv);
%Boundary Conditions
f(x,y)=x^2-y^2;
b1=xv(1:n);
b2=yv(1:m);
u(1:n,1)=f(b1,1)
u(1:n,m)=f(b1,4)
u(1,1:m)=f(1,b2)
u(n,1:m)=f(9,b2)
% u(n,1:m) is a matrix with interior zeros (perimeter is filled by boundary conditions), here
% a is my attempt to define variables to assign to the elements in u(n,1:m) which are zero
a=sym('a',[n m]);
%Trying to calculate system of equations accounting for boundary conditions and elements
% which may be 0 that I wish to actually represent a variable (if the entry u(i,j) = 0 then
% I wish to assign this instead as u(i,j)=a(i,j) where a is a symbolic variable
for i=2:n-1
    for j=2:m-1
        if u(i,j)==0
           if u(i+1,j)==0
             if u(i,j+1)==0
               if u(i-1,j)==0
                 if u(i,j-1)==0
                    u(i,j-1)=a(i,j-1);
                  u(i-1,j)=a(i-1,j);
                u(i,j+1)=a(i,j+1);
              u(i+1,j)=a(i+1,j);
            u(i,j)=a(i,j);
                 end
               end
             end
           end
        end
      C=(((1/h)+(0.1)*yv(j))*u(i+1,j)+...
            ((1/k)+(0.1)*xv(i))*u(i,j+1)-...
            ((2/h)+(2/k)+(0.1)*(xv(i)+yv(j)))*u(i,j)+((1/h)*u(i-1,j))+...
            ((1/k)*u(i,j-1)))
    end
end
% These are the first few results I get from the output
C =
 
271/25
 
 
C =
 
-21/25
 
 
C =
 
-129/100
% It finally begins to construc equations but some of them seem to be missing variables, and
% the first equation is in terms of a(3,3), not a(2,2) which is what I want
C =
 
4*a2_3 + 20*a3_2 - (2413*a3_3)/50 + (403*a3_4)/20 + (411*a4_3)/100
 
 
C =
 
20*a3_3 - (9653*a3_4)/200
 
 
C =
 
20*a3_4
 
 
C =
 
4*a2_6 + 20*a3_5 - (1931*a3_6)/40 + (403*a3_7)/20 + (33*a4_6)/8

Best Answer

 if u(i,j)==0
           if u(i+1,j)==0
             if u(i,j+1)==0
               if u(i-1,j)==0
                 if u(i,j-1)==0
                   u(i,j-1)=a(i,j-1);
                 end
                   u(i-1,j)=a(i-1,j);
               end
                   u(i,j+1)=a(i,j+1);
           end
                 u(i+1,j)=a(i+1,j);
           end
                 u(i,j)=a(i,j);
      end
Use following type. May be this is what you're want
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