Index in position 1 exceeds array bounds. Index must not exceed 1000.

When I run this program I get an error by line 44 saying "Index in position 1 exceeds array bounds. Index must not exceed 1000."

Can somebody please explain to me what this error means and how to fix it?

M=1000;
dx=.02;
Tmax=10;
dt=.01;
N=Tmax/dt; %number of time steps
h0=0.1;
g=9.81;
St=.1;
Cf=0.005;
W=1;

%Creating an arrays for A,h,u,B,C
h=zeros(M,N);
A=zeros(M,N);
u=zeros(M,N);
B=zeros(M,N);
C=zeros(M,N);

%Initial Conditions
for n=1
    for i=1:M %for t=0 aka n=1
        h(i,n)=h0; %the height of the water is given at h0
        A(i,n)=0; %the speed of the water is 0 tf A=0
        u(i,n)=A(i,n)./h(i,n);
        B(i,n)=h(i,n).*(u(i,n)).^2+g.*h(i,n).^2./2;
        C(i,n)=-St.*g.*h(i,n)-(Cf.*u(i,n).*abs(u(i,n))/2).*(W+2.*h(i,n))./W;
    end
end

%Left Boundry
for n=1:N-1
    h(1,n+1)=h(2,n)-(dt./dx).*A(2,n);
    A(1,n+1)=0;
    u(1,n+1)=A(1,n+1)./h(1,n+1);
    B(1,n+1)=h(1,n+1).*(u(1,n+1)).^2+g.*h(1,n+1).^2./2;
    C(1,n+1)=-St.*g.*h(1,n+1)-(Cf.*u(1,n+1).*abs(u(1,n+1))/2).*(W+2.*h(1,n+1))./W;
end

%Main Equations
for n=1:N-1
    for i=2:M
        h(i,n+1)=.5.*(h(i+1,n)+h(i-1,n))-(dt./2.*dx).*(A(i+1,n)-A(i-1,n));
        A(i,n+1)=.5.*(A(i+1,n)+A(i-1,n))-(dt./2.*dx).*(B(i+1,n)-B(i-1,n))+.5.*(C(i+1,n)+C(i-1,n)).*dt;
        u(i,n+1)=A(i,n+1)./h(i,n+1);
        B(i,n+1)=h(i,n+1).*(u(i,n+1)).^2+g.*h(i,n+1).^2/2;
        C(i,n+1)=-St.*g.*h(i,n+1)-(Cf.*u(i,n+1).*abs(u(i,n+1))./2).*(W+2.*h(i,n+1))./W;
    end
end

%Right Boundry
for n=1:N-1
    h(M,n+1)=h(M-1,n)+(dt./dx).*A(M-1,n);
    A(M,n+1)=0;
    u(M,n+1)=A(M,n+1)./h(M,n+1);
    B(M,n+1)=h(M,n+1).*(u(M,n+1)).^2+g.*h(M,n+1).^2./2;
    C(M,n+1)=-St.*g.*h(M,n+1)-(Cf.*u(M,n+1).*abs(u(M,n+1))./2).*(W+2.*h(1,n+1))./W;
end

Answer 1

[Voss]

%Main Equations
for n=1:N-1
    for i=2:M
        h(i,n+1)=.5.*(h(i+1,n)+h(i-1,n))-(dt./2.*dx).*(A(i+1,n)-A(i-1,n));
        % ...
    end
end

When i == M, the code will try to access h(i+1,n), which is h(M+1,n), which will fail and generate the error because h has only M rows. (Similarly for A(i+1,n) later on that same line.)

Changing the for loop to for i=2:M-1 avoids this problem and allows the code to run completely without throwing any errors, and that seems like it's probably the correct thing to do, since h(M,:), A(M,:), etc., are calculated in the next section ("Right Boundry").