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paper.bib
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paper.bib
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@article{2012_optimal_stability_polynomials,
Author = {Ketcheson, David I. and Ahmadia, Aron J.},
Journal = {Communications in Applied Mathematics and Computational Science},
Number = {2},
Pages = {247--271},
Title = {Optimal stability polynomials for numerical integration of initial value problems},
Volume = {7},
doi = {10.2140/camcos.2012.7.247},
Year = {2012}
}
@article{2009_monotonicity,
Author = {Ketcheson, David I.},
Journal = {Mathematics of Computation},
Month = sep,
Number = {267},
Pages = {1497--1513},
Title = {{Computation of optimal monotonicity preserving general linear methods}},
Volume = {78},
doi = {10.1090/S0025-5718-09-02209-1},
Year = {2009}}
@inproceedings{parsani-eccomas,
Author = {Parsani, Matteo and Ketcheson, David I. and Deconinck, W.},
Booktitle = {{Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering}},
Month = {September},
Title = {Explicit {R}unge-{K}utta schemes for the spectral difference method applied to wave propagation problems},
Year = {2012}}
@inproceedings{Parsani_finnish,
Author = {Parsani, Matteo and Ketcheson, David I.},
Booktitle = {{Proceedings of the 11th Finnish Mechanics Days}},
Month = {November},
Pages = {1--5},
Title = {Optimized low-order explicit {R}unge-{K}utta schemes for high-order spectral difference method},
Year = {2012}}
@article{2013_sd_erk,
Author = {Parsani, Matteo and Ketcheson, David I. and Deconinck, W.},
Journal = {SIAM Journal on Scientific Computing},
Month = jul,
Number = {2},
Pages = {A957-A986},
Title = {Optimized explicit {R}unge-{K}utta schemes for the spectral difference method applied to wave propagation problems},
Volume = {35},
doi = {10.1137/120885899},
Year = {2013}}
@article{2014_ssp_rkdg,
Author = {Kubatko, Ethan J. and Yeager, Benjamin A. and Ketcheson, David I.},
Journal = {Journal of Scientific Computing},
Number = {2},
Pages = {313-344},
Title = {Optimal strong-stability-preserving {R}unge--{K}utta time discretizations for discontinuous {G}alerkin methods},
Volume = {60},
doi = {10.1007/s10915-013-9796-7},
Year = {2014}}
@article{conde2017implicit,
title={Implicit and implicit--explicit strong stability preserving {R}unge--{K}utta methods with high linear order},
author={Conde, Sidafa and Gottlieb, Sigal and Grant, Zachary J and Shadid, John N},
journal={Journal of Scientific Computing},
volume={73},
number={2-3},
pages={667--690},
year={2017},
doi = {10.1007/s10915-017-0560-2},
publisher={Springer}
}
@inproceedings{2018_wso,
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 J and Moxey, David and Peir{\'o}, Joaquim and Vincent, Peter E and Schwab, Christoph},
Title = {DIRK Schemes with High Weak Stage Order},
Year = {2018}}
@article{christlieb2016explicit,
title={Explicit strong stability preserving multistage two-derivative time-stepping schemes},
author={Christlieb, Andrew J and Gottlieb, Sigal and Grant, Zachary and Seal, David C.},
journal={Journal of Scientific Computing},
volume={68},
number={3},
pages={914--942},
year={2016},
doi={10.1007/s10915-016-0195-8},
publisher={Springer}
}
@article{gottlieb2015optimal,
title={Optimal explicit strong stability preserving {R}unge--{K}utta methods with high linear order and optimal nonlinear order},
author={Gottlieb, Sigal and Grant, Zachary and Higgs, Daniel},
journal={Mathematics of Computation},
volume={84},
number={296},
pages={2743--2761},
doi={10.1007/s10915-016-0195-8},
year={2015}
}
@article{grant2019strong,
title={A strong stability preserving analysis for explicit multistage two-derivative time-stepping schemes based on Taylor series conditions},
author={Grant, Zachary and Gottlieb, Sigal and Seal, David C.},
journal={Communications on Applied Mathematics and Computation},
volume={1},
number={1},
pages={21--59},
year={2019},
doi={10.1007/s10915-016-0195-8},
publisher={Springer}
}
@inproceedings{reynoso2017strong,
title={Strong stability preserving sixth order two-derivative {R}unge--{K}utta methods},
author={Reynoso, Gustavo Franco and Gottlieb, Sigal and Grant, Zachary J},
booktitle={{AIP Conference Proceedings}},
volume={1863},
number={1},
pages={560068},
year={2017},
doi={10.1063/1.4992751},
organization={AIP Publishing LLC}
}
@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},
Title = {Solving ordinary differential equations {II}: Stiff and differential-algebraic problems},
Volume = {14},
Year = {1996}
}
@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},
Volume = {229},
doi = {10.1016/j.jcp.2009.11.006},
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{2017_msrk,
Author = {Bresten, Christopher and Gottlieb, Sigal and Grant, Zachary and Higgs, Daniel and Ketcheson, David I. and N{\'e}meth, Adrian},
Journal = {Mathematics of Computation},
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,
title={Optimal Monotonicity-Preserving Perturbations of a Given {R}unge--{K}utta Method},
author={Higueras, Inmaculada and Ketcheson, David I. and Kocsis, Tiham{\'e}r A},
journal={Journal of Scientific Computing},
volume={76},
number={3},
pages={1337--1369},
year={2018},
publisher={Springer},
doi={10.1007/s10915-018-0664-3}
}
@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{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}
}
@misc{cvx,
author = {Michael Grant and Stephen Boyd},
title = {{CVX}: Matlab Software for Disciplined Convex Programming, version 2.1},
howpublished = {\url{http://cvxr.com/cvx}},
month = mar,
year = 2014
}
@incollection{gb08,
author = {Michael Grant and Stephen Boyd},
title = {Graph implementations for nonsmooth convex programs},
booktitle = {Recent Advances in Learning and Control},
series = {Lecture Notes in Control and Information Sciences},
editor = {V. Blondel and S. Boyd and H. Kimura},
publisher = {Springer-Verlag Limited},
pages = {95--110},
year = 2008,
doi = {10.1007/978-1-84800-155-8_7},
url = {http://stanford.edu/~boyd/graph_dcp.html}
}
@Article{higueras2019new,
Author = {I. {Higueras} and T. {Rold\'an}},
Title = {{New third order low-storage SSP explicit Runge-Kutta methods}},
FJournal = {{Journal of Scientific Computing}},
Journal = {{Journal of Scientific Computing}},
ISSN = {0885-7474; 1573-7691/e},
Volume = {79},
Number = {3},
Pages = {1882--1906},
Year = {2019},
Publisher = {Springer US, New York, NY},
Language = {English},
MSC2010 = {65L06 65L05 65L04},
Zbl = {1418.65079}
}
@Article{higueras2019strong,
Author = {I. {Higueras} and T. {Rold\'an}},
Title = {{Strong stability preserving properties of composition Runge-Kutta schemes}},
FJournal = {{Journal of Scientific Computing}},
Journal = {{J. Sci. Comput.}},
ISSN = {0885-7474; 1573-7691/e},
Volume = {80},
Number = {2},
Pages = {784--807},
Year = {2019},
Publisher = {Springer US, New York, NY},
Language = {English},
MSC2010 = {65L05 65L06 65L20 65M20},
Zbl = {1416.65193},
doi = {10.1007/s10915-019-00916-3}
}