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# 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:

```#Pkg.add("DiffEqProblemLibrary")
using DiffEqProblemLibrary
prob = prob_dae_resrob
sol = solve(prob,IDA())```