DAE Problems

# 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,u,p,t,du)`). 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{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.

### 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())``````