# DAE Problems

## Mathematical Specification of an DAE Problem

To define a DAE Problem, you simply need to give the function $f$ and the initial condition $u₀$ which define an ODE:

\[0 = f(du,u,p,t)\]

`f`

should be specified as `f(du,u,p,t)`

(or in-place as `f(resid,du,u,p,t)`

). 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.

## Problem Type

### Constructors

`DAEProblem(f::DAEFunction,du0,u0,tspan)`

`DAEProblem{isinplace}(f,du0,u0,tspan)`

: Defines the DAE with the specified functions.`isinplace`

optionally sets whether the function is inplace or not. This is determined automatically, but not inferred.

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

### Fields

`f`

: The function in the ODE.`du0`

: The initial condition for the derivative.`u0`

: The initial condition.`tspan`

: The timespan for the problem.`callback`

: A callback to be applied to every solver which uses the problem. Defaults to a black CallbackSet, which will have no effect.`differential_vars`

: A logical array which declares which variables are the differential (non algebraic) vars (i.e.`du'`

is in the equations for this variable). Defaults to nothing. Some solvers may require this be set if an initial condition needs to be determined.

## Example Problems

Examples problems can be found in DiffEqProblemLibrary.jl.

To use a sample problem, such as `prob_dae_resrob`

, you can do something like:

```
#]add DiffEqProblemLibrary
using DiffEqProblemLibrary, Sundials
prob = prob_dae_resrob
sol = solve(prob,IDA())
```