Error: Incorrect dimensions for matrix multiplication

I have the following code which is an iterative solver that solves for a linear poisson's equation as a simple test:

clearvars; clc; close all;
N=30;
[D,x] = cheb(N); D2 = D^2;
D2(N+1,:) = D(N+1,:); %Neumann BC at left endpoint (x=-1), esp w/ D
D2 = D2(2:N+1,2:N+1); %Dirichlet BC at right endpoint (x=1)

u = (exp(4*x) - 4*exp(-4)*(x-1)-exp(4))/16; %w/ BCs ux(-1)=u(1)=0
n =ones(size(u));
%build source term
dndx = D *n; 

dudx = D *u;
prod1 = dndx .* dudx;
du2dx = D * dudx;
prod2 = n .*du2dx;

invN = (1./n) ;

source =  prod1(2:N) + prod2(2:N);


uold = ones(size(u(2:N))); 
max_iter =500; 
err_max = 1e-8; 

 for iterations = 1:max_iter
    phikmax_old = (max(abs(uold)));
    duoldx = D(2:N,2:N) *uold;
 
    dnudx = dndx(2:N) .* duoldx;
    ffh = source; 
    RHS = ffh - dnudx; 
    Stilde = invN(2:N) .* RHS; 

    unew = D2\[Stilde;0];
   
    phikmax = (max(abs(unew)));

    if phikmax < err_max 
        it_error = err_max /2;
    else
        it_error = abs( phikmax - phikmax_old) / phikmax;
    end
    if it_error < err_max
        break;
    end
    
    uold = unew;

 end
unew = [0;unew]; 
figure
plot(x,unew,'--rs',x,(u));
legend('Num solution','Exact solution')

Function cheb:

function [ D, x ] = cheb ( N )
  if ( N == 0 )
    D = 0.0;
    x = 1.0;
    return
  end

  x = cos ( pi * ( 0 : N ) / N )'; 

  c = [ 2.0; ones(N-1,1); 2.0 ] .* (-1.0).^(0:N)';
  X = repmat ( x, 1, N + 1 );
  dX = X - X';
  D = ( c * (1.0 ./ c )' ) ./ ( dX + ( eye ( N + 1 ) ) );
  D = D - diag ( sum ( D' ) );

  return
end

I get the correct solution at the first iteraion " for iterations = 1 %1:max_iter" then after that I get the error:

Error using  * 
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of
rows in the second matrix. To perform elementwise multiplication, use '.*'.

Error in Filename (line 298)
    duoldx = D(2:N,2:N) *uold;

which I believe it has to do with uold not being same size as unew? How can I fix that? Thanks

[Mathieu NOE]

hello

your array uold has length = 29 at the first iteration and 30 at the second (when you do: uold = unew;)

there is something to fix in your code when you update some data as their dimensions change (and should not) as the loop iterates

Answer 1

[Torsten]

You set uold = unew, but unew is 30x1 instead of 29x1.

Since D(2:N,2:N) is 29x29, MATLAB errors in the next iteration when you try to compute

duoldx = D(2:N,2:N) *uold;

[Janee]

I can see that it's just I am not sure how to adjust it to work.

[Torsten]

Maybe by setting

uold = unew(2:N);

instead of

uold = unew;

?

But it's just to make the code work technically without knowledge about what you have programmed.