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additional references
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ranocha committed Jul 12, 2020
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24 changes: 23 additions & 1 deletion paper.bib
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Expand Up @@ -69,7 +69,7 @@ @article{conde2017implicit


@inproceedings{2018_wso,
Author = {Ketcheson, David and Seibold, Benjamin and Shirokoff, David and Zhou, Dong},
Author = {Ketcheson, David I. and Seibold, Benjamin and Shirokoff, David and Zhou, Dong},
Booktitle = {Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018},
Editor = {Sherwin, Spencer et. al.w},
Title = {DIRK Schemes with High Weak Stage Order},
Expand Down Expand Up @@ -209,3 +209,25 @@ @article{conde2018embedded
journal={arXiv preprint arXiv:1806.08693},
year={2018}
}

@article{vermeire2019optimal,
title={Optimal {R}unge--{K}utta schemes for pseudo time-stepping with
high-order unstructured methods},
author={Vermeire, Brian C and Loppi, Niki A and Vincent, Peter E},
journal={Journal of Computational Physics},
volume={383},
pages={55--71},
year={2019},
publisher={Elsevier},
doi={10.1016/j.jcp.2019.01.003}
}

@article{vermeire2020optimal,
title={Optimal embedded pair {R}unge--{K}utta schemes for pseudo-time stepping},
author={Vermeire, Brian C and Loppi, Niki A and Vincent, Peter E},
journal={Journal of Computational Physics},
pages={109499},
year={2020},
publisher={Elsevier},
doi={10.1016/j.jcp.2020.109499}
}
11 changes: 6 additions & 5 deletions paper.md
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Expand Up @@ -44,7 +44,7 @@ The original (and still primary) focus of the package is on the design of
Runge-Kutta methods, but some routines for designing other classes of methods
are also included.

# Statement of need
# Statement of need

Over the last several decades, a great deal of work has gone into the design
of numerical ODE solvers. Initially this work was aimed at developing general
Expand Down Expand Up @@ -129,14 +129,14 @@ enabling its efficient solution for methods with many steps.

# Related research and software

`RK-Opt` development has proceeded in close connection to the `NodePy` package.
Whereas `RK-Opt` is focused on the design of numerical methods, `NodePy` is focused
`RK-Opt` development has proceeded in close connection to the `NodePy` package (https://github.com/ketch/NodePy).
Whereas `RK-Opt` is focused on the design of numerical methods, `NodePy` is focused
more on their analysis. A common workflow involves generating new methods with
`RK-Opt` and then studying their properties in more detail using `NodePy`.

Some of the research projects that have made use of `RK-Opt` include development of:

- SSP Runge-Kutta methods
- SSP Runge-Kutta methods
[@2008_explicit_ssp;@2009_implicit_ssp;@gottlieb2015optimal]
- SSP linear multistep methods [@2009_monotonicity]
- SSP general linear methods [@2011_tsrk;@2017_msrk]
Expand All @@ -145,10 +145,11 @@ Some of the research projects that have made use of `RK-Opt` include development
- Optimal Runge-Kutta stability polynomials [@2012_optimal_stability_polynomials]
- Additive and downwind SSP Runge-Kutta methods [@2011_dwssp;@2018_perturbations]
- Optimal Runge-Kutta methods for specific PDE semi-discretizations [@parsani-eccomas;@Parsani_finnish;@2013_sd_erk;@2014_ssp_rkdg]
- Optimal Runge-Kutta methods for pseudo-time stepping [@vermeire2019optimal;@vermeire2020optimal]
- Embedded pairs for Runge-Kutta methods [@conde2018embedded]
- Runge-Kutta methods with high weak stage order [@2018_wso]
- SSP multistage, multiderivative methods [@christlieb2016explicit;@grant2019strong;@reynoso2017strong]

As can be seen from this list, applications have mostly stemmed from the
work of the main developer's research group, but have since expanded
beyond that.
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