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:
and an initial guess $u₀$ of where
f should be specified as
f(u,p,t) (or in-place as
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
isinplace optionally sets whether the function is inplace or not. This is determined automatically, but not inferred. Additionally, the constructor from
ODEProblems is provided:
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.
f: The function in the ODE.
u0: The initial guess for the steady state.
p: The parameters for the problem. Defaults to
kwargs: The keyword arguments passed onto the solves.
Special Solution Fields
SteadyStateSolution type is different from the other DiffEq solutions because it does not have temporal information.