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paper.bib
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@phdthesis{jin2019higher,
title={Higher order stabilized time stepping in unfitted finite element method on moving domains},
author={Jin, Xingren},
year={2019},
school={Georg-August-Universit{\"a}t G{\"o}ttingen}
}
@mastersthesis{horvathembedded,
title={Embedded pairs for optimal strong stability preserving {R}unge--{K}utta methods},
author={Horv{\'a}th, Akos},
year={2019},
school={Eötvös Loránd Tudományegyetem}
}
@phdthesis{norton2015structure,
title={Structure-preserving General Linear Methods},
author={Norton, Terence James Taylor},
year={2015},
school={University of Bath}
}
@book{hairer1993,
Address = {Berlin},
Author = {Hairer, Ernst and N\o rsett, Syvert P. and Wanner, G.},
Edition = {Second},
Publisher = {Springer},
Series = {Springer Series in Computational Mathematics},
Title = {Solving ordinary differential equations {I}: Nonstiff Problems},
Year = {1993}
}
@book{Hairer:ODEs2,
Address = {Berlin},
Author = {Hairer, Ernst and Wanner, G.},
Edition = {Second},
Publisher = {Springer},
Series = {Springer Series in Computational Mathematics},
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@article{2008_explicit_ssp,
Author = {Ketcheson, David I.},
Journal = {SIAM Journal on Scientific Computing},
Number = {4},
Pages = {2113--2136},
Title = {Highly Efficient Strong Stability Preserving {R}unge-{K}utta Methods with Low-Storage Implementations},
Volume = {30},
doi = {10.1137/07070485X},
Year = {2008}}
@article{2009_implicit_ssp,
Author = {Ketcheson, David I. and Macdonald, Colin B. and Gottlieb, Sigal},
Journal = {Applied Numerical Mathematics},
Month = feb,
Number = {2},
Pages = {373--392},
Title = {Optimal implicit strong stability preserving {R}unge--{K}utta methods},
Volume = {59},
doi = {10.1016/j.apnum.2008.03.034},
Year = {2009}}
@article{2010_LSRK,
Author = {Ketcheson, David I.},
Journal = {Journal of Computational Physics},
Month = mar,
Number = {5},
Pages = {1763--1773},
Title = {{R}unge--{K}utta methods with minimum storage implementations},
doi = {10.1016/j.jcp.2009.11.006},
Volume = {229},
Year = {2010}}
@article{2011_dwssp,
Author = {Ketcheson, David I.},
Journal = {SIAM Journal on Numerical Analysis},
Month = may,
Number = {4},
Pages = {1649},
Title = {{Step Sizes for Strong Stability Preservation with Downwind-Biased Operators}},
Volume = {49},
doi = {10.1137/100818674},
Year = {2011}}
@article{2011_tsrk,
Author = {Ketcheson, David I. and Gottlieb, Sigal and Macdonald, Colin B.},
Journal = {SIAM Journal on Numerical Analysis},
Month = jun,
Number = {6},
Pages = {2618-2639},
Title = {Strong Stability Preserving Two-step {R}unge--{K}utta Methods},
Volume = {49},
doi = {10.1137/10080960X},
Year = {2011}}
@article{2013_effective_order_ssp,
Author = {Hadjimichael, Yiannis and Macdonald, Colin B. and Ketcheson, David I. and Verner, J. H.},
Journal = {SIAM Journal on Numerical Analysis},
Number = {4},
Pages = {2149--2165},
Title = {Strong Stability Preserving Explicit {R}unge--{K}utta Methods of Maximal Effective Order},
Volume = {51},
doi = {10.1137/120884201},
Year = {2013}}
@article{2014_internal_stability,
Author = {Ketcheson, David I. and L{\'o}czi, Lajos and Parsani, Matteo},
Journal = {SINUM},
Number = {5},
Pages = {2227--2249},
Title = {Internal error propagation in explicit {R}unge--{K}utta methods},
Volume = {52},
doi = {10.1137/130936245},
Year = {2014}}
@article{2014_hork,
Author = {Ketcheson, David I. and {bin Waheed}, Umair},
Journal = {CAMCoS},
Number = {2},
Pages = {175-200},
Title = {A comparison of high order explicit {R}unge-{K}utta, extrapolation, and deferred correction methods in serial and parallel},
Volume = {9},
doi = {10.2140/camcos.2014.9.175},
Year = {2014}}
@article{2016_ssp_lmm_vss,
Author = {Hadjimichael, Yiannis and Ketcheson, David I. and L{\'o}czi, Lajos and N{\'e}meth, Adri{\'a}n},
Journal = {Siam Journal On Numerical Analysis},
Number = {5},
Pages = {2799-2832},
Title = {Strong stability preserving explicit linear multistep methods with variable step size},
Volume = {54},
doi = {10.1137/15M101717X},
Year = {2016}}
@article{2017_dense,
Author = {Ketcheson, David I. and L{\'o}czi, Lajos and Jangabylova, Aliya and Kusmanov, Adil},
Journal = {Journal of Scientific Computing},
Number = {3},
Pages = {944--958},
Title = {Dense output for strong stability preserving {R}unge--{K}utta methods},
Volume = {71},
doi = {10.1007/s10915-016-0331-5},
Year = {2017}}
@article{2017_msrk,
Author = {Bresten, Christopher and Gottlieb, Sigal and Grant, Zachary and Higgs, Daniel and Ketcheson, David I. and N{\'e}meth, Adrian},
Journal = {Math. of Comp.},
Pages = {747-769},
Title = {Strong Stability Preserving Multistep {R}unge-{K}utta Methods},
Volume = {86},
doi = {10.1090/mcom/3115},
Year = {2017}}
@article{2018_perturbations,
Author = {Higueras, Inmaculada and Ketcheson, David I. and Kocsis, Tiham{\'e}r A.},
Journal = {Journal of Scientific Computing},
Number = {3},
Pages = {1337--1369},
Title = {Optimal Monotonicity-Preserving Perturbations of a Given {R}unge--{K}utta Method},
Volume = {76},
doi = {10.1007/s10915-018-0664-3},
Year = {2018}}
@article{2018_sspalmm,
Author = {Hadjimichael, Yiannis and Ketcheson, David I.},
Journal = {Math. of Comp.},
Number = {313},
Pages = {2295--2320},
Title = {Strong-stability-preserving additive linear multistep methods},
Volume = {87},
doi = {10.1090/mcom/3296},
Year = {2018}}
@article{meurer2017sympy,
title={SymPy: symbolic computing in Python},
author={Meurer, Aaron and Smith, Christopher P. and Paprocki, Mateusz and {\v{C}}ert{\'\i}k, Ond{\v{r}}ej and Kirpichev, Sergey B. and Rocklin, Matthew and Kumar, AMiT and Ivanov, Sergiu and Moore, Jason K. and Singh, Sartaj and others},
journal={PeerJ Computer Science},
volume={3},
pages={e103},
year={2017},
doi = {10.7717/peerj-cs.103},
publisher={PeerJ Inc.}
}
@book{oliphant2006guide,
title={A guide to NumPy},
author={Oliphant, Travis E.},
volume={1},
year={2006},
publisher={Trelgol Publishing USA}
}
@article{walt2011numpy,
title={The NumPy array: a structure for efficient numerical computation},
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volume={13},
number={2},
pages={22--30},
year={2011},
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}
@article{hunter2007matplotlib,
title={Matplotlib: A 2D graphics environment},
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@article{ranocha2019some,
title={Some notes on summation by parts time integration methods},
author={Ranocha, Hendrik},
journal={Results in Applied Mathematics},
volume={1},
pages={100004},
year={2019},
doi={10.1016/j.rinam.2019.100004},
publisher={Elsevier}
}
@article{conde2018embedded,
title={Embedded error estimation and adaptive step-size control for optimal explicit strong stability preserving {R}unge--{K}utta methods},
author={Conde, Sidafa and Fekete, Imre and Shadid, John N},
journal={arXiv preprint arXiv:1806.08693},
year={2018}
}
@article{nusslein2020positivity,
title={Positivity-Preserving Adaptive {R}unge-{K}utta Methods},
author={N{\"u}{\ss}lein, Stephan and Ranocha, Hendrik and Ketcheson, David I.},
journal={arXiv preprint arXiv:2005.06268},
year={2020}
}
@article{2019_energyRRK,
Author = {Ketcheson, David I.},
Journal = {SIAM Journal on Numerical Analysis},
Number = {6},
Pages = {2850-2870},
Title = {Relaxation {R}unge-Kutta Methods: {C}onservation and stability for Inner-Product Norms},
Volume = {57},
doi = {10.1137/19M1263662},
Year = {2019}}
@article{ketcheson2020more,
title={More efficient time integration for Fourier pseudospectral {DNS} of incompressible turbulence},
author={Ketcheson, David I. and Mortensen, Mikael and Parsani, Matteo and Schilling, Nathanael},
journal={International Journal for Numerical Methods in Fluids},
volume={92},
number={2},
pages={79--93},
year={2020},
doi={10.1002/fld.4773},
publisher={Wiley Online Library}
}
@article{ketcheson2020RK-Opt,
title={{RK-Opt}: {A} package for the design of numerical {ODE} solvers},
author={Ketcheson, David I and Parsani, Matteo and Grant, Zachary J and
Ahmadia, Aron and Ranocha, Hendrik},
journal={Journal of Open Source Software},
year={2020},
month={10},
volume={5},
number={54},
pages={2514},
publisher={The Open Journal},
doi={10.21105/joss.02514},
url={https://github.com/ketch/RK-Opt},
version={1.0}
}