Steady State Problems

Steady State Problems

Mathematical Specification of a Steady State Problem

To define an Steady State Problem, you simply need to give the function $f$ which defines the ODE:

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

and an initial guess $u₀$ of where f(u,p,t)=0. f should be specified as f(u,p,t) (or in-place as f(du,u,p,t)), 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.

Note that for the steady-state to be defined, we must have that f is autonomous, that is f is independent of t. But the form which matches the standard ODE solver should still be used. The steady state solvers interpret the f by fixing t=0.

Problem Type

Constructors

SteadyStateProblem(f::ODEFunction,u0)
SteadyStateProblem{isinplace}(f,u0)

isinplace optionally sets whether the function is inplace or not. This is determined automatically, but not inferred. Additionally, the constructor from ODEProblems is provided:

SteadyStateProblem(prob::ODEProblem)

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

Fields

Special Solution Fields

The SteadyStateSolution type is different from the other DiffEq solutions because it does not have temporal information.