Indexing exceeds matrix dimensions - error on 2 lines of code

I keep getting an error on lines 54 & 55 (where I calculate dCc and Cc). Code is to do Holly-Preissmann method of river modeling (2 loops, time and space).

%clear workspace
clear
clc

%define variables
xmin = 0;   %given
xmax = 2;   %placeholder
N = 100;    %grid nodes
dt = 0.009; %time step (smaller is better for precision)
t = 0;      %given
Tmax = 0.5; %placeholder
v = 1;      %velocity placeholder
s = .05;    %from boundary condition equation

%function domain
dx = (xmax - xmin)/N;
x = xmin-dx : dx : xmax+dx;

%initial conditions 
c0 = 10*exp(-(x-.5).^2/(2*s^2));  %boundary condition
%c = c0;
dC = 0;
C = c0;
dCc = 0;
Cc = 0;

%calculate loop through time
nsteps = Tmax/dt;

for n = 1 : nsteps

      %calculate boundary
  %    dC(1) = dC(3);
      C(1) = C(3);
  %    dC(N+3) = dC(N+1);
      C(N+3) = C(N+1);
      for i = 2 : N+2

      %calculate loop through space
      nsteps = N;

      for n = 1 : nsteps
          for j = 2 : N+2
              c = x(j) - v*dt;
              r = (x(j) - c)/dx;
              a1 = (r^2)*(3 - 2*r);
              a2 = 1 - a1;
              a3 = (r^2)*(1 - r)*dx;
              a4 = -r*((1-r)^2)*dx;
              b1 = 6*r*(r-1)/dx;
              b2 = -b1;
              b3 = r*(3*r-2);
              b4 = (1-r)*(3*r-1);
              dCc(j) = b1*C(j-1) + b2*C(j) - b3*dC(j-1) + b4*dC(j); %error here
              Cc = a1*C(j-1) + a2*C(j) + a3*dC(j-1) + a4*dC(j); %error here
          end
          %update new x and C for step
          x = x + dx;
          dC = dCc;
          C = Cc;
      end
      end
      %update new t for step
      t = t + dt;

      %calculate exact solution
      exact = 10*exp(-(x-.5-(v*t)).^2/(2*s^2)); %exact solution

      %plot both exact and initial solution
      plot(x,exact,'r-')
      hold on
      plot(x,C,'bo-','markerfacecolor','b');
      hold off
      axis([xmin xmax -0.5 10])      %sets axis min and max
      xlabel('x','fontsize',14)     %x axis label, set font size
      ylabel('C(t,x)','fontsize',14) %y axis label, set font size
      title(sprintf('time = %1.3f',t),'fontsize',14)  %shows time for distance x
      shg
      pause(dt)

end

[Jan]

Please do not let us guess, which are the lines 54 and 55 and how you can have errors in 2 lines, although Matlab will stop at the first error already. Post the error message instead, such that we do not have to guess the details. If you use the "{} Code" button, the code would be readable. I really really really cannot understand, how so many users post unreadable code and simply do not care about this. It should be your interest to provide readable code. Weird.

Answer 1

[Roger Stafford]

I see one error. In the two lines where an error occurs you are referencing dC(j) where j = 2 on the first trip through the surrounding loop. However, dC has been defined as a scalar, dC = 0, so dC(2) is not defined. Hence the error message. You need to somehow define dC for all indices from 1 to nsteps.

[Elaine Brewer]

Thanks. This got me part of the way there. Then I had written an extra loop. Still doing a weird oscillation but getting closer.

[Image Analyst]

If you're still getting errors, please post ALL the red text.