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8 changes: 4 additions & 4 deletions docs/src/basics/faq.md
Original file line number Diff line number Diff line change
Expand Up @@ -12,9 +12,9 @@ For guidelines on debugging ODE solve issues, see
First of all, don't panic. You may have experienced one of the following warnings:

> dt <= dtmin. Aborting. There is either an error in your model specification or the true solution is unstable.
>
>
> NaN dt detected. Likely a NaN value in the state, parameters, or derivative value caused this outcome.
>
>
> Instability detected. Aborting

These are all pointing to a similar behavior: for some reason or another, the
Expand Down Expand Up @@ -185,7 +185,7 @@ numerically and thus results in much better performance. This is seen in many in
SciMLBenchmarks. Thus it is recommended that in almost all or most situations, one should use the
mass matrix form of the DAE solver.

However, it is generally recommended that if you are solving a DAE that you use
However, it is generally recommended that if you are solving a DAE that you use
[ModelingToolkit.jl](https://mtk.sciml.ai/dev/) because it has many utilities for pre-processing
DAEs to make them more numerically stable. For example, if your algebraic conditions are not
uniquely matching to algebraic variables (i.e. you have at least one unique algebraic variable
Expand Down Expand Up @@ -455,7 +455,7 @@ thing you can do is use

You can't. For floating-point numbers, you shouldn't use below `abstol=1e-14`
and `reltol=1e-14`. If you need lower than that, use arbitrary precision numbers
like BigFloats or [ArbFloats.jl](https://github.com/JuliaArbTypes/ArbFloats.jl).
like BigFloats or [ArbNumerics.jl](https://github.com/JeffreySarnoff/ArbNumerics.jl).

## Autodifferentiation and Dual Numbers

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2 changes: 1 addition & 1 deletion docs/src/basics/overview.md
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Expand Up @@ -31,7 +31,7 @@ timespan and `BigFloat` for specifying the initial condition, then the solution
will solve using `Rational{BigInt}` for the timesteps and `BigFloat` for the
independent variables. A wide variety of number types are compatible with the
solvers such as complex numbers, unitful numbers (via Unitful.jl),
decimals (via DecFP), dual numbers, and many more which may not have been tested
decimals (via [DecFP](https://github.com/JuliaMath/DecFP.jl)), dual numbers, and many more which may not have been tested
yet (thanks to the power of multiple dispatch!). For information on type-compatibility,
please see the solver pages for the specific problems.

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2 changes: 1 addition & 1 deletion docs/src/features/callback_functions.md
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Expand Up @@ -522,7 +522,7 @@ However, at some point we will hit machine epsilon, the value where
`t + eps(t) == t`, so we cannot measure infinitely many bounces and instead will
be limited by the floating-point accuracy of our number representation. Using
alternative number types like
[ArbFloats.jl](https://github.com/JuliaArbTypes/ArbFloats.jl) can allow for this
[ArbNumerics.jl](https://github.com/JeffreySarnoff/ArbNumerics.jl) can allow for this
to be done at very high accuracy, but still not infinite. Thus, what we need to
do is determine a tolerance after which we assume the accumulation has been
reached and define the exit behavior. In this case, we will say when the
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4 changes: 2 additions & 2 deletions docs/src/index.md
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Expand Up @@ -42,7 +42,7 @@ DifferentialEquations.jl integrates with the Julia package sphere with:
- Automatic plotting of time series and phase plots
- Built-in interpolations
- Wraps for common C/Fortran methods like Sundials and Hairer's radau
- Arbitrary precision with BigFloats and Arbfloats
- Arbitrary precision with BigFloats and [ArbNumerics.jl](https://github.com/JeffreySarnoff/ArbNumerics.jl)
- Arbitrary array types, allowing the definition of differential equations on
matrices and distributed arrays
- Unit checked arithmetic with Unitful
Expand All @@ -67,7 +67,7 @@ Additionally, DifferentialEquations.jl comes with built-in analysis features, in
for guidance on PRs, issues, and other matters relating to contributing to SciML.
- See the [SciML Style Guide](https://github.com/SciML/SciMLStyle) for common coding practices and other style decisions.
- There are a few community forums:

+ The #diffeq-bridged and #sciml-bridged channels in the
[Julia Slack](https://julialang.org/slack/)
+ The #diffeq-bridged and #sciml-bridged channels in the
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10 changes: 5 additions & 5 deletions docs/src/solvers/ode_solve.md
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Expand Up @@ -71,7 +71,7 @@ At medium tolerances (`>1e-8`?) it is recommended you use `Rodas5P`,
`Rodas4P` (the former is more efficient, but the latter is more reliable),
`Kvaerno5`, or `KenCarp4`. As native DifferentialEquations.jl solvers,
many Julia numeric types (such as BigFloats,
[ArbFloats](https://github.com/JuliaArbTypes/ArbFloats.jl), or
[ArbNumerics.jl](https://github.com/JeffreySarnoff/ArbNumerics.jl), or
[DecFP](https://github.com/JuliaMath/DecFP.jl)) will work. When the equation is
defined via the `@ode_def` macro, these will be the most efficient.

Expand Down Expand Up @@ -960,22 +960,22 @@ using IRKGaussLegendre
`IRKGL16(;kwargs...)` has the following arguments:

- second_order_ode (boolean):

+ =false (default): for a ODEProblem type
+ =true: for a second-order differential equation

- simd (boolean):

+ =true: SIMD-vectorized implementation only available for Float32 or Float64 computations
+ =false (default): generic implementation that can use with arbitrary Julia-defined number systems
- mstep: output saved at every 'mstep' steps. Default 1.
- initial_extrapolation: initialization method for stages.

+ =false: simplest initialization
+ =true (default): extrapolation from the stage values of previous step
- maxtrials: maximum number of attempts to accept adaptive step size
- threading

+ =false (default): sequential execution of the numerical integration
+ =true: computations using threads (shared memory multi-threading) for stage-wise parallelization

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