# 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 to`I`

, the`UniformScaling`

identity matrix.

## Special Solution Fields

The `SteadyStateSolution`

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