understanding DDE23 function format

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alpedhuez
alpedhuez on 1 May 2020
Edited: alpedhuez on 4 May 2020
DDE23 function has a format of
ddex1de(t,y,Z)
How should one understand Z?

Accepted Answer

Guru Mohanty
Guru Mohanty on 4 May 2020
我理解你试图解决系统of differential equation using ‘dde23’. To do this you need to do following steps.
  1. Define constant delays.
In this system of equation there are two lags i.e. (t-1) and (t-0.2).
lags = [1 0.2];
2. Define Solution History.
It Defines the first solution from which the solver starts iterations.
functions = history(t)
s = ones(3,1);
end
3. Form the equation.
functiondydt = ddex1de(t,y,Z)
ylag1 = Z(:,1);
ylag2 = Z(:,2);
dydt = [ylag1(1);
ylag1(1)+ylag2(2);
y(2)];
end
Here In the call to ddex1de,
‘t’ is a scalar indicates the current ‘t’ in the equation
‘y’ is a column vector approximates y(t)
‘Z’ is a column vector approximates y(t – α j ) for delay α j = lags(J).
In the following example Solution history is [1;1;1]. So Approximate values of lag ie ‘Z’ will be a matrix of size 3x2.In ‘Z’ Row defines the number of equations and column defines Number of lags.
4. Solve using ‘dde23’.
tspan = [0 5];
sol = dde23(@ddefun, lags, @history, tspan);
2 Comments
Guru Mohanty
Guru Mohanty on 4 May 2020
As it is a System of 3 Equations, 'y', 'dydt', 'ylag1' 'ylag2' have dimension 3x1. There are two constant Delay present, So The dimention of 'Z' is 3x2.

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