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unify references
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ranocha committed Sep 27, 2021
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2 changes: 1 addition & 1 deletion README.md
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A collection of functionality around [B-series](https://en.wikipedia.org/wiki/Butcher_group) in [Julia](https://julialang.org/). See

- Philippe Chartier, Ernst Hairer, Gilles Vilmart (2010)
Algebraic Structures of B-series
Algebraic Structures of B-series.
Foundations of Computational Mathematics
[DOI: 10.1007/s10208-010-9065-1](https://doi.org/10.1007/s10208-010-9065-1)

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30 changes: 19 additions & 11 deletions src/BSeries.jl
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Expand Up @@ -21,7 +21,7 @@ export elementary_differentials
# This is a dirty workaround until the performance bugfix
# https://github.com/JuliaLang/julia/pull/42300
# is merged
@static if v"1.6" <= VERSION < v"1.7.0-rc2"
@static if v"1.6" <= VERSION < v"1.8.0"
Base.hastypemax(::Type{Bool}) = true
end

Expand All @@ -36,7 +36,7 @@ formed by substituting the B-series `b` into the B-series `a`.
Section 3.2 of
- Philippe Chartier, Ernst Hairer, Gilles Vilmart (2010)
Algebraic Structures of B-series
Algebraic Structures of B-series.
Foundations of Computational Mathematics
[DOI: 10.1007/s10208-010-9065-1](https://doi.org/10.1007/s10208-010-9065-1)
"""
Expand All @@ -61,7 +61,7 @@ formed by composing the B-series `a` with the B-series `b`.
Section 3.1 of
- Philippe Chartier, Ernst Hairer, Gilles Vilmart (2010)
Algebraic Structures of B-series
Algebraic Structures of B-series.
Foundations of Computational Mathematics
[DOI: 10.1007/s10208-010-9065-1](https://doi.org/10.1007/s10208-010-9065-1)
"""
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The coefficients of the B-series returned by this method need to be multiplied
by the corresponding elementary differential of the input vector field ``f``.
See Section 3.2 of
# References
Section 3.2 of
- Philippe Chartier, Ernst Hairer, Gilles Vilmart (2010)
Algebraic Structures of B-series
Algebraic Structures of B-series.
Foundations of Computational Mathematics
[DOI: 10.1007/s10208-010-9065-1](https://doi.org/10.1007/s10208-010-9065-1)
"""
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Here, `u` is assumed to be a vector of variables from Symbolics.jl (`Symbolics.Num`)
and `f` is assumed to be a vector of expressions in these variables.
See Section 3.2 of
# References
Section 3.2 of
- Philippe Chartier, Ernst Hairer, Gilles Vilmart (2010)
Algebraic Structures of B-series
Algebraic Structures of B-series.
Foundations of Computational Mathematics
[DOI: 10.1007/s10208-010-9065-1](https://doi.org/10.1007/s10208-010-9065-1)
"""
Expand Down Expand Up @@ -235,9 +239,11 @@ of the original ODE.
The coefficients of the B-series returned by this method need to be multiplied
by the corresponding elementary differential of the input vector field ``f``.
See Section 3.2 of
# References
Section 3.2 of
- Philippe Chartier, Ernst Hairer, Gilles Vilmart (2010)
Algebraic Structures of B-series
Algebraic Structures of B-series.
Foundations of Computational Mathematics
[DOI: 10.1007/s10208-010-9065-1](https://doi.org/10.1007/s10208-010-9065-1)
"""
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Here, `u` is assumed to be a vector of variables from Symbolics.jl (`Symbolics.Num`)
and `f` is assumed to be a vector of expressions in these variables.
See Section 3.2 of
# References
Section 3.2 of
- Philippe Chartier, Ernst Hairer, Gilles Vilmart (2010)
Algebraic Structures of B-series
Algebraic Structures of B-series.
Foundations of Computational Mathematics
[DOI: 10.1007/s10208-010-9065-1](https://doi.org/10.1007/s10208-010-9065-1)
"""
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