MATLAB Mathematics - SERC - Index of

5 Differential Equations
The example solves the equations on [0,5] with history
y 1 () t = 1
y 2 () t = 1
y 3 () t = 1
for t ≤ 0 .
Note The demo ddex1 contains the complete code for this example. To see the
code in an editor, click the example name, or type edit ddex1 at the command
line. To run the example type ddex1 at the command line. See “DDE Solver
Basic Syntax” on page 5-52 for more information.
1 Rewrite the problem as a first-order system. To use dde23, you must
rewrite the equations as an equivalent system of first-order differential
equations. Do this just as you would when solving IVPs and BVPs for ODEs
(see “Examples: Solving Explicit ODE Problems” on page 5-9). However, this
example needs no such preparation because it already has the form of a
first-order system of equations.
2 Identify the lags. The delays (lags) τ 1 , …,
τ k are supplied to dde23 as a
vector. For the example we could use
lags = [1,0.2];
In coding the differential equations, τ j = lags(j).
3 Code the system of first-order DDEs. Once you represent the equations as
a first-order system, and specify lags, you can code the equations as a
function that dde23 can use.
This code represents the system in the function, ddex1de.
function dydt = ddex1de(t,y,Z)
ylag1 = Z(:,1);
ylag2 = Z(:,2);
5-54