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Improve DAE solver discussion of interpolations #706

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Dec 11, 2023
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Improve DAE solver discussion of interpolations #706

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15 changes: 6 additions & 9 deletions docs/src/solvers/dae_solve.md
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# DAE Solvers
# Mass Matrix and Fully Implicit DAE Solvers

## Recommended Methods

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!!! note

The standard Hermite interpolation used for ODE methods in OrdinaryDiffEq.jl
is not applicable to the algebraic variables. Thus, for the following mass-matrix
methods, use the interpolation (thus `saveat`) with caution if the default
Hermite interpolation is used. All methods which mention a specialized interpolation
(and implicit ODE methods) are safe.
falls back to a linear interpolation on the differential variables. If the
mass matrix is non-diagonal, the Hermite interpolation does not have a fallback
and will error.

#### Rosenbrock Methods

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- `ROS34PW3` - A 4th order strongly A-stable (Rinf~0.63) Rosenbrock-W method.

!!! note


`Rosenbrock23` and `Rosenbrock32` have a stiff-aware interpolation but this interpolation is not safe for the algebraic variables.
Thus use the interpolation (thus `saveat`) with caution if the default Hermite interpolation is used.
`Rosenbrock23` and `Rosenbrock32` have a stiff-aware interpolation but this interpolation is not safe for the algebraic variables.
Thus use the interpolation (and therefore `saveat`) with caution if the default Hermite interpolation is used.

#### FIRK Methods

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