dde23: Derivative and history vectors have different lengths.

Hi, I'm trying to solve a very basic set of time-delay differential equations with dde23. All my code is below. collFunc2 is the driver, which sets three time lags -- taui, taug, tauf -- and calls dde23 on the set of three coupled differential equations -- dnidt -- in collFunc2. The history values are constant and zero in coll2hist. When I try to run this I get 'Derivative and history vectors have different lengths.' Both seem to be three columns long to me. What am I doing wrong? Thanks so much for any help. - Sylvia

function sol = collision2
    taui = 15*60;
    taug = 30*60; % graupel growth time 
    tauf = 10*60; % fallout time
    lags = [taui, taui + taug, taui + taug + tauf];
    sol = dde23(@collFunc2,lags,@coll2hist,[0,1000]);

      function [t,dnidt] = collFunc2(t,y,Z)
      alpha = 2.4*10^(-5); % volume sweep out rate [m3 s-1]
      N = 50; % multiplication rate
      ylag1 = Z(:,1); ylag2 = Z(:,2); ylag3 = Z(:,3);

      dnidt(1) = alpha*N*((y(2)*y(3) - ylag1(2)*ylag1(3)));
      dnidt(2) = alpha*N*(ylag1(2)*ylag1(3) - ylag2(2)*ylag2(3));
      dnidt(3) = alpha*N*(ylag2(2)*ylag2(3) - ylag3(2)*ylag3(3));  

      function s = coll2hist(~)
      % Constant history function 
      s = [0; 0; 0];

Answer 1

[Walter Roberson]

The output of the delay differential equation is expected to have a single output that is a column vector that is the derivatives. Instead you have two outputs, the first of which is a copy of the time. But the time is a scalar, and a scalar does not match the history vector size of being a 3x1 vector.

[Sylvia]

Thank you, Walter. I changed the collFunc2 header to

function dnidt = collFunc2(t,y,Z)

Now I get an error which says that 'DDEs must return column vectors' .. yes, that's what dnidt is, right? Why the complaint? - Sylvia

[Walter Roberson]

No, you created dnidt as a row vector. When you have a scalar and you extend it by assigning to the second element using

A(2) = VALUE

then the result is a row vector.

You can assign

dnidt = zeros(3,1);

or you can assign to

dnidt(2,1) = value;

or you can use

dnidt = dnidt.'

at the end.

[Sylvia]

Thanks, Walter. I just transposed dnidt.