The solution to the delayed differential equations using the code dde23 represents the solution by the third order Runge-Kutta method or what?

dde23

Answer 1

[Sam Chak]

Hi @mohammed,

Your guess is correct. If you click on the link to the dde23's Algorithm section, you will find that it states "dde23 tracks discontinuities and integrates with the explicit Runge-Kutta (2,3) pair and interpolant of ode23. It uses iteration to take steps longer than the lags."

If you wish to delve deeper into this topic, I would encourage you to refer to the following academic papers:

1. L. F. Shampine and S. Thompson, “Solving DDEs in MATLAB,” Applied Numerical Mathematics, vol. 37, no. 4, pp. 441–458, Jun. 2001, doi: 10.1016/s0168-9274(00)00055-6.
2. P. Bogacki and L. F. Shampine, “A 3(2) pair of Runge - Kutta formulas,” Applied Mathematics Letters, vol. 2, no. 4, pp. 321–325, 1989, doi: 10.1016/0893-9659(89)90079-7.

[mohammed]

@Sam Chak Thank you so much

Answer 2

[Steven Lord]

It's not clear to me what information you're looking for. The dde23 function returns the solution to a system of delay differential equations.

If you're asking what algorithm it uses, see the Algorithms section on that documentation page for a brief description and the References section on that documentation page for references to one book and one tutorial that provide more detailed information.