Code covered by the BSD License  

Highlights from
Tutorial on solving DDEs with DDE23

  • exam1
  • exam1
  • exam2
  • exam2
  • exam3
  • exam3
  • exam4
  • exam4
  • exam5
  • exam5
  • exam6 This is a demonstration problem for CTMS/BD in
  • exam6 This is a demonstration problem for CTMS/BD in
  • exam7 An example from C. Marriott and C. DeLisle, Effects
  • exam7 An example from C. Marriott and C. DeLisle, Effects
  • exam8 This is the suitcase problem from Suherman, et al.,
  • exam8 This is the suitcase problem from Suherman, et al.,
  • exer1 Example 1 of K.W. Neves, Automatic integration
  • exer1 Example 1 of K.W. Neves, Automatic integration
  • exer2 Example of J.D. Farmer, Chaotic Attractors of an
  • exer2 Example of J.D. Farmer, Chaotic Attractors of an
  • exer3 Wheldon's model of chronic granuloctic leukemia
  • exer3 Wheldon's model of chronic granuloctic leukemia
  • exer5
  • exer5
  • exer6 Sample problem of ARCHI manual. The absolute error
  • exer6 Sample problem of ARCHI manual. The absolute error
  • exer7 Marchuk immunology model of E. Hairer, S.P. Norsett, and
  • exer7 Marchuk immunology model of E. Hairer, S.P. Norsett, and
  • prob1 This system of ODE's is taken from 'An Introduction to Nuermcial Methods
  • prob1 This system of ODE's is taken from 'An Introduction to Nuermcial Methods
  • prob2 This problem considers a cardiovascular model, which can be found in
  • prob2 This problem considers a cardiovascular model, which can be found in
  • prob2b This problem considers a cardiovascular model, which can be found in
  • prob2b This problem considers a cardiovascular model, which can be found in
  • prob3 This problem is epidemic model due to Cooke, more information can be
  • prob3 This problem is epidemic model due to Cooke, more information can be
  • prob4 This problem is an epidemic model due to Cooke et alia, more information
  • prob4 This problem is an epidemic model due to Cooke et alia, more information
  • prob5 This problem population growth model due to Cooke et alia, more information
  • prob5 This problem population growth model due to Cooke et alia, more information
  • View all files

Tutorial on solving DDEs with DDE23

by

 

22 Aug 2003 (Updated )

Solving delay differential equations with DDE23. Tutorial + Examples.

prob4
function sol = prob4
%  This problem is an epidemic model due to Cooke et alia, more information
%  can be found in 'Interaction of maturation delay and nonlinear birth in
%  population and epidemic models' J. Math. Biol., 39 (1999) 332-352.
%  (This is reference 3 of the tutorial).

% Copyright 2002, The MathWorks, Inc.

T = 0.2;
lambda = 12;
sol = dde23(@prob4f,T,[2; 3.5],[0, 25],[],lambda,T);

figure
plot(sol.x,sol.y)
legend('I(t)','N(t)',0)
title(['Problem 4. Cooke et al. Epidemic Model with ' ...
       ' \lambda = ',num2str(lambda),'.'])
xlabel('time t')

%-----------------------------------------------------------------------

function yp = prob4f(t,y,Z,lambda,T)
%PROB4F  The derivative function for Problem 4 of the DDE Tutorial.
a  = 1;
b  = 80;
d  = 1;
d1 = 1;
e  = 10;
gamma = 0.5;

I = y(1);
N = y(2);
Nlag = Z(2,1);
dIdt = lambda*(N - I)*(I/N) - ( d + e + gamma)*I;
dNdt = b*exp(-a*Nlag)*Nlag*exp(-d1*T) - d*N - e*I;
yp = [ dIdt; dNdt];

Contact us