DDE Problems

DDE Problems

Mathematical Specification of a DDE Problem

To define a DDE Problem, you simply need to give the function $f$ and the initial condition $u0$ which define an ODE:

\[du = f(u,p,t,h)\]

f should be specified as f(u,h,p,t) (or in-place as f(du,u,h,p,t)). h is the history function which is accessed for all delayed values. For example, the ith component delayed by a time tau is denoted by h(t-tau). Note that we are not limited to numbers or vectors for u0; one is allowed to provide u0 as arbitrary matrices / higher dimension tensors as well.

Functional Forms for h

h, the history function, can be called the following ways:

Note that a dispatch for the supplied history function of matching form is required for whichever function forms are used in the user derivative function f.

Declaring Lags

Lags are declared separately from their use. One can use any lag by simply using the interpolant of h at that point. However, one should use caution in order to achieve the best accuracy. When lags are declared, the solvers can more efficiently be more accurate and thus this is recommended.

Problem Type



isinplace optionally sets whether the function is inplace or not. This is determined automatically, but not inferred.