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

RODEProblem{isinplace}(f,u0,tspan,noise=WHITE_NOISE,rand_prototype=nothing,callback=nothing,mass_matrix=I) : Defines the RODE with the specified functions. The default noise is WHITE_NOISE. isinplace optionally sets whether the function is inplace or not. This is determined automatically, but not inferred.

### Fields

• f: The drift function in the SDE.

• u0: The initial condition.

• tspan: The timespan for the problem.

• noise: The noise process applied to the noise upon generation. Defaults to Gaussian white noise. For information on defining different noise processes, see the noise process documentation page

• rand_prototype: A prototype type instance for the noise vector. It defaults to nothing, which means the problem should be interpreted as having a noise vector whose size matches u0.

• 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.