RODE Problems

RODE Problems

Mathematical Specification of a RODE Problem

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

\[\frac{du}{dt} = f(u,p,t,W(t))\]

where W(t) is a random process. f should be specified as f(u,p,t,W) (or in-place as f(du,u,p,t,W)), and u₀ should be an AbstractArray (or number) whose geometry matches the desired geometry of u. 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.

Constructors

Parameters are optional, and if not given then a NullParameters() singleton will be used which will throw nice errors if you try to index non-existent parameters. Any extra keyword arguments are passed on to the solvers. For example, if you set a callback in the problem, then that callback will be added in every solve call.

For specifying Jacobians and mass matrices, see the DiffEqFunctions page.

Fields