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:

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

`f` should be specified as `f(t,u,h)` (or in-place as `f(t,u,h,du)`). `h` is the history function which is accessed for all delayed values. For example, the `i`th 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.

## Problem Type

### Constructors

``````ConstantLagDDEProblem(f,h,u0,lags,tspan,callback=nothing,mass_matrix=I)
DDEProblem(f,h,u0,lags,tspan,callback=nothing,mass_matrix=I)``````

### Fields

• `f`: The function in the ODE.

• `h`: The history function for the ODE before `t0`.

• `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 `I`, the `UniformScaling` identity matrix.