https://github.com/ranocha/bseries.jl
Computing with B-series in Julia
https://github.com/ranocha/bseries.jl
average-vector-field b-series backward-error-analysis energy-preservation hacktoberfest julia modified-equations modifying-integrators runge-kutta
Last synced: 11 months ago
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Computing with B-series in Julia
- Host: GitHub
- URL: https://github.com/ranocha/bseries.jl
- Owner: ranocha
- License: mit
- Created: 2021-09-17T13:46:52.000Z (almost 5 years ago)
- Default Branch: main
- Last Pushed: 2024-04-22T07:04:02.000Z (about 2 years ago)
- Last Synced: 2024-04-23T08:59:28.951Z (about 2 years ago)
- Topics: average-vector-field, b-series, backward-error-analysis, energy-preservation, hacktoberfest, julia, modified-equations, modifying-integrators, runge-kutta
- Language: Julia
- Homepage: https://ranocha.github.io/BSeries.jl
- Size: 4.15 MB
- Stars: 25
- Watchers: 5
- Forks: 3
- Open Issues: 20
-
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE.md
- Citation: CITATION.bib
- Security: SECURITY.md
Awesome Lists containing this project
README
# BSeries
[](https://ranocha.de/BSeries.jl/stable)
[](https://ranocha.de/BSeries.jl/dev)
[](https://github.com/ranocha/BSeries.jl/actions?query=workflow%3ACI)
[](https://coveralls.io/github/ranocha/BSeries.jl?branch=main)
[](https://codecov.io/gh/ranocha/BSeries.jl)
[](https://opensource.org/licenses/MIT)
[](https://doi.org/10.5281/zenodo.5534602)
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.
Foundations of Computational Mathematics
[DOI: 10.1007/s10208-010-9065-1](https://doi.org/10.1007/s10208-010-9065-1)
## API Documentation
The API of [BSeries.jl](https://github.com/ranocha/BSeries.jl) is documented in
the [online documentation](https://ranocha.de/BSeries.jl/stable). Information
on each function is available in their docstrings.
BSeries.jl re-exports everything from
[RootedTrees.jl](https://github.com/SciML/RootedTrees.jl).
However, if you rely on functionality from that package, you should also include
it explicitly in your project dependencies to track breaking changes, since the
version numbers of RootedTrees.jl and BSeries.jl are not necessarily synchronized.
The main API of BSeries.jl consists of the following components.
- B-series behave like `AbstractDict`s mapping `RootedTree`s to coefficients.
- The B-series of time integration methods such as Runge-Kutta methods
can be constructed by the function `bseries`.
- Vector space operations (addition/subtraction and multiplication by scalars)
are available.
- The algebraic structures of the composition law and the substitution law are
implemented via `compose` and `substitute`.
- Backward error analysis can be performed via `modified_equation`s and
`modifying_integrator`s.
Please consult the documentation or the docstrings for further information.
Please note that B-series analysis is most conveniently applied to the
autonomous form of ordinary differential equations (ODEs). Thus, BSeries.jl and
RootedTrees.jl usually assume that time integration methods give the same
result, independent of whether an ODE is written in an autonomous or a
non-autonomous form. For Runge-Kutta methods, this means that the usual row-sum
assumption is used.
## Referencing
If you use
[BSeries.jl](https://github.com/ranocha/BSeries.jl)
for your research, please cite it using the bibtex entry
```bibtex
@article{ketcheson2023computing,
title={Computing with {B}-series},
author={Ketcheson, David I and Ranocha, Hendrik},
journal={ACM Transactions on Mathematical Software},
volume={49},
number={2},
year={2023},
month={06},
doi={10.1145/3573384},
eprint={2111.11680},
eprinttype={arXiv},
eprintclass={math.NA}
}
```
In addition, you can also refer to BSeries.jl directly as
```bibtex
@misc{ranocha2021bseries,
title={{BSeries.jl}: {C}omputing with {B}-series in {J}ulia},
author={Ranocha, Hendrik and Ketcheson, David I},
year={2021},
month={09},
howpublished={\url{https://github.com/ranocha/BSeries.jl}},
doi={10.5281/zenodo.5534602}
}
```
## License and contributing
This project is licensed under the MIT license (see [LICENSE.md](LICENSE.md)).
Since it is an open-source project, we are very happy to accept contributions
from the community. Please refer to [CONTRIBUTING.md](CONTRIBUTING.md) for more
details.