How to solve delay differential equations with computed history (not constant)
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Greetings!
I'm trying to solve some delay differential equations. The classic example, the Lotka-Volterra predation model illustrates the problem. This is solved in many places around the web*, always using a constant history (as far as I can tell). Usually, the ode system is solved for comparison, then the delayed system, using a constant history, like the last computed point of the ode system. I'd like to use that computed (approximated by, say, ode45, not analytical) solution of the non-delayed system as history, but can't figure out how. Help would be much appreciated.
* e.g., https://www.mathworks.com/matlabcentral/fileexchange/3899-tutorial-on-solving-ddes-with-dde23
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Accepted Answer
Torsten
on 19 Jun 2023
Moved: Torsten
on 19 Jun 2023
Save the results of the non-delayed ode in arrays T and Y, create an interpolation function
fun_history = @(t) interp1(T,Y,t)
pass this function to the history function of the delay ode solver (e.g. dde23) and evaluate it at the given time instants passed to the history function.
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