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:

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

where W(t) is a random process. f should be specified as f(t,u,W) (or in-place as f(t,u,W,du)), 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.


RODEProblem(f,u0,tspan,noise=WHITE_NOISE,noise_prototype=nothing,callback=nothing,mass_matrix=I) : Defines the RODE with the specified functions. The default noise is WHITE_NOISE.