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:
f should be specified as
f(t,u,h) (or in-place as
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.
f: The function in the ODE.
h: The history function for the ODE before
lags: An array of lags. For constant lag problems this should be numbers. For state-dependent delay problems this is a tuple of functions.
tspan: The timespan for the problem.
callback: A callback to be applied to every solver which uses the problem. Defaults to nothing.
mass_matrix: The mass-matrix. Defaults to