How to solve delay differential equations with computed history (not constant)

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pedro 2023-6-19

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https://ww2.mathworks.cn/matlabcentral/answers/1985114-how-to-solve-delay-differential-equations-with-computed-history-not-constant

评论： pedro 2023-6-19

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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Answer 1

Torsten 2023-6-19

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https://ww2.mathworks.cn/matlabcentral/answers/1985114-how-to-solve-delay-differential-equations-with-computed-history-not-constant#answer_1258664

移动：Torsten 2023-6-19

在 MATLAB Online 中打开

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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pedro 2023-6-19

Torsten,

Thank you very much for your assistance. I had to massage your history function a bit, but in the end it worked. Thanks again, for giving me a push in the right direction!

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