Index in position 2 exceeds array bounds (must not exceed 1001)

I have the following code with the error:

Index in position 2 exceeds array bounds (must not exceed 1001)

my code

dx = 0.001; %initially from Sod paper. grid/cell size
L = 1; %domain length 
x = 0:dx:L;
N = length(x); % number of grids 
NEQ = 8; % how many equ 
U = zeros(NEQ,N);

Error in function:

function [ U_L, U_R] = MUSCL(U,N,NEQ )
size_U = size(U);
U_L = zeros(size_U); 
U_R = zeros(size_U);

delta = 1e-6; % epsilon 

for i= 1:NEQ
    for j = 2:N-1
        denom_L = (U(i,j) - U(i,j-1)); 
        denom_R = (U(i,j+2) - U(i,j+1)); % error here

        denom_L = sign(denom_L+1e-64)*max(delta, abs(denom_L)); % sign 

        denom_R = sign(denom_R+1e-64)*max(delta, abs(denom_R));
        r_L = (U(i,j) - U(i,j-1))/denom_L;

        r_R = (U(i,j+2) - U(i,j+1))/denom_R; % divide by 0 check ?

        theta_L = Limiter(r_L);
        theta_R = Limiter(r_R);

    end

end

for j = 2:N-1
    
    U_L(:,j) = U(:,j)+0.5*theta_R.*(U(:,j)-U(:, j-1)); % error 
    U_R(:,j) = U(:,j+1)-0.5*theta_L.*(U(:,j+2)-U(:,j+1));% 
    

end

How do I fix this? How can I write the correct "domain" to loop over such setup.

Answer 1

[DGM]

U is 8x1001.

i spans [1 8]

j spans [2 1000]

but you index ahead of j by 2.

U(i,j+2)

You'd either have to stop at 999 (i.e. 2:N-2) or pad the array. You'll have to decide what's contextually appropriate.

[Jamie Al]

I was trying to "pad" the array but I really don't think I know how. I keep getting indexing errors

[DGM]

If U needs to be one element wider, initialize it one element wider. If it doesn't need to stay that wide afterwards, trim off the last column.

[Jamie Al]

Do you mind showing a small example?

[DGM]

Make U one column wider:

U = zeros(NEQ,N+1);

Trim one column off the end:

U_L = U_L(:,1:end-1);
U_R = U_R(:,1:end-1);

You'll have to make sure that's appropriate for your use.