Error - Index in position 1 exceeds array bounds (must not exceed 10)

I am trying to run this code and I keep getting this error:

"Index in position 1 exceeds array bounds (must not exceed 10).

Error in WaveEquation (line 21)

x1(row,col) = 2*(1-r)*x1(row, col)+r*(x1(row+1,col)+x1(row-1,col))-x1(row,col-1); "

I tried to debug it and I am getting nowhere. I think I know what is happening; I believe that the error occurs as it is TRYING to continue to row 10. Attached is the debugging for code/table.

clear all; format compact; tic
delx = 0.1;
r = 1;
u = 1;
delt = r.^2*delx/u;         % Delta Time Step Size
Tsteps = round(1/delt);     % Number of Steps

x1 = zeros(Tsteps, 1/(2*delx)+2);

% Initial Conditions
x = 0:delx:.5+delx;
x1(1,:) = sin(pi*x);

% Boundary Conditions
x1(2,2:end-1) = .5*(x1(1,1:end-2)+x1(1,3:end));
x1(2,end) = x1(2,end-2);                                              % Reflection Line

for row = 3:size(x1,1)
   for col = 2:size(x1,2)-1
       x1(row,col) = 2*(1-r)*x1(row, col)+r*(x1(row+1,col)+x1(row-1,col))-x1(row,col-1);
   end
   x1(row,end) = x1(row,end-2);                                      % Reflection Line
end

x2 = [x1,fliplr(x1(:,1:end-3))];

figure(1),imagesc(0:delx:1,(0:delt:Tsteps*delt),x2),colorbar
    ylabel('\leftarrow time (sec)')
    xlabel('x')
    title('Hyperbolic PDE')
   
if (delx==.1)
    dispmat = [x1(1:8,1:7)];
    fprintf('\nCompare to table 3.5, Solution of wave equation\n')
    disp(num2str(dispmat))
end

Answer 1

[the cyclist]

I think you want

for row = 3:size(x1,1)-1
   
end

instead of

for row = 3:size(x1,1)
   
end

so that you don't try to access an element beyond the end of the array, when you use row+1.

You seem to have done it correctly for the loop over columns.