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(t,u)=0
. f
should be specified as f(t,u)
(or in-place as f(t,u,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.
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,u0,mass_matrix=I)
Additionally, the constructor from the ODEProblem
is provided:
SteadyStateProblem(prob::ODEProblem)
Fields
f
: The function in the ODE.u0
: The initial guess for the steady state.mass_matrix
: The mass-matrix. Defaults toI
, theUniformScaling
identity matrix.
Special Solution Fields
The SteadyStateSolution
type is different from the other DiffEq solutions because it does not have temporal information.