DI Dr. Sebastian Falkensteiner

Research Area

Differential Algebra, Algebraic Geometry, Symbolic Computation

WWW

Personal homepage

Co-Organizer of the Diff.-Equations and Singularities Seminar: https://sites.google.com/view/diffeq-and-sing/

Software

FirstOrderSolve

A Maple package for computing local and algebraic solutions of first order autonomous AODEs

This Maple package computes power series, Puiseux series and algebraic solutions of first order autonomous ordinary differential equations where the unknown function and its derivative fulfill a polynomial equation. The standard commands of Maple might not find these solutions and ...

Authors: Sebastian Falkensteiner

More Software Website

Publications

2023

[Falkensteiner]

The algebro-geometric method: Solving algebraic differential equations by parametrizations

S. Falkensteiner, J.J. Mitteramskogler, R. Sendra, F. Winkler

Bulletin of the American Mathematical Society, pp. 1-41. 2023. ISSN 0273-0979.

[bib]

@article{RISC6507,
author = {S. Falkensteiner and J.J. Mitteramskogler and R. Sendra and F. Winkler},
title = {{The algebro-geometric method: Solving algebraic differential equations by parametrizations}},
language = {english},
journal = {Bulletin of the American Mathematical Society},
pages = {1--41},
isbn_issn = {ISSN 0273-0979},
year = {2023},
refereed = {yes},
length = {41}
}

2022

[Falkensteiner]

On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry

S. Falkensteiner, C. Garay-Lopez, M. Haiech, M. P. Noordman, F. Boulier, Z. Toghani

Journal of Symbolic Computation 115, pp. 53-73. 2022. ISSN: 0747-7171. [doi]

[bib]

@article{RISC6335,
author = {S. Falkensteiner and C. Garay-Lopez and M. Haiech and M. P. Noordman and F. Boulier and Z. Toghani},
title = {{On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {115},
pages = {53--73},
isbn_issn = {ISSN: 0747-7171},
year = {2022},
refereed = {yes},
keywords = {Differential Algebra, Tropical Differential Algebraic Geometry, Power Series Solutions, Newton Polyhedra, Arc Spaces, Tropical Differential Equations, Initial forms of Differential Polynomials},
length = {21},
url = {https://doi.org/10.1016/j.jsc.2022.08.005}
}

[Falkensteiner]

On Formal Power Series Solutions of Algebraic Ordinary Differential Equations

S. Falkensteiner, Yi Zhang, N. Thieu Vo

Mediterranean Journal of Mathematics 19(74), pp. 1-16. March 2022. ISSN 1660-5446. [doi]

[bib]

@article{RISC6490,
author = {S. Falkensteiner and Yi Zhang and N. Thieu Vo},
title = {{On Formal Power Series Solutions of Algebraic Ordinary Differential Equations}},
language = {english},
journal = {Mediterranean Journal of Mathematics},
volume = {19},
number = {74},
pages = {1--16},
isbn_issn = {ISSN 1660-5446},
year = {2022},
month = {March},
refereed = {yes},
keywords = {Formal power series, algebraic differential equation.},
length = {16},
url = {https://doi.org/10.1007/s00009-022-01984-w}
}

[Falkensteiner]

Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables

J. Cano, S. Falkensteiner, D. Robertz, R. Sendra

Journal of Symbolic Computation 114, pp. 1-17. 2022. ISSN 1095-855X. [doi]

[bib]

@article{RISC6501,
author = {J. Cano and S. Falkensteiner and D. Robertz and R. Sendra},
title = {{Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {114},
pages = {1--17},
isbn_issn = {ISSN 1095-855X},
year = {2022},
refereed = {yes},
length = {17},
url = {http://doi.org/10.1016/j.jsc.2022.04.012}
}

[Falkensteiner]

Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs

S. Falkensteiner

In: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Amir Hashemi (ed.), Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC), ISSAC '22 , pp. 63-71. 2022. Association for Computing Machinery, ISBN 9781450386883. [doi]

[bib]

@inproceedings{RISC6585,
author = {S. Falkensteiner},
title = {{Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs}},
booktitle = {{Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation}},
language = {english},
series = {ISSAC '22},
pages = {63--71},
publisher = {Association for Computing Machinery},
isbn_issn = {ISBN 9781450386883},
year = {2022},
editor = {Amir Hashemi},
refereed = {yes},
length = {9},
conferencename = {International Symposium on Symbolic and Algebraic Computation (ISSAC)},
url = {https://doi.org/10.1145/3476446.3536185}
}

2021

[Falkensteiner]

Existence and convergence of Puiseux series solutions for first order autonomous differential equations

J. Cano, S. Falkensteiner, R. Sendra

Journal of Symbolic Computation 108, pp. 137-151. 2021. ISSN 0747-7171. [doi]

[bib]

@article{RISC6262,
author = {J. Cano and S. Falkensteiner and R. Sendra},
title = {{Existence and convergence of Puiseux series solutions for first order autonomous differential equations}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {108},
pages = {137--151},
isbn_issn = {ISSN 0747-7171},
year = {2021},
refereed = {yes},
keywords = {Algebraic differential equation, Algebraic curve, Place, Formal Puiseux series solution, Convergent solution},
length = {15},
url = {http://doi.org/10.1016/j.jsc.2020.06.010}
}

[Falkensteiner]

Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs - A MAPLE Package

F. Boulier, J. Cano, S. Falkensteiner, R. Sendra

In: Communications in Computer and Information Science, Rob Corless, Jürgen Gerhard and Ilias Kotsireas (ed.), Proceedings of Maple Conference 20201414, pp. 89-103. 2021. Springer, Cham, ISSN 1865-0929. [url]

[bib]

@inproceedings{RISC6334,
author = {F. Boulier and J. Cano and S. Falkensteiner and R. Sendra},
title = {{Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs - A MAPLE Package}},
booktitle = {{Communications in Computer and Information Science}},
language = {english},
volume = {1414},
pages = {89--103},
publisher = {Springer, Cham},
isbn_issn = {ISSN 1865-0929},
year = {2021},
editor = {Rob Corless and Jürgen Gerhard and Ilias Kotsireas},
refereed = {yes},
keywords = {Maple, Symbolic computation, Algebraic differential equation, Formal Puiseux series solution, Algebraic solution},
length = {15},
conferencename = {Maple Conference 2020},
url = {doi.org/10.1007/978-3-030-81698-8_7}
}

[Falkensteiner]

On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry

F. Boulier, S. Falkensteiner, M.P. Noordman, O.L. Sanchez

In: International Workshop on Computer Algebra in Scientific Computing, F. Boulier, M. England, T. Sadykov, E. Vorozhtsov (ed.), Proceedings of Computer Algebra in Scientific Computing, pp. 62-77. 2021. Springer, ISSN 0302-9743. [doi]

[bib]

@inproceedings{RISC6337,
author = {F. Boulier and S. Falkensteiner and M.P. Noordman and O.L. Sanchez},
title = {{On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry}},
booktitle = {{International Workshop on Computer Algebra in Scientific Computing}},
language = {english},
pages = {62--77},
publisher = {Springer},
isbn_issn = {ISSN 0302-9743},
year = {2021},
editor = {F. Boulier and M. England and T. Sadykov and E. Vorozhtsov},
refereed = {yes},
length = {16},
conferencename = {Computer Algebra in Scientific Computing},
url = {https://doi.org/10.1007/978-3-030-85165-1_5}
}

2020

[Falkensteiner]

Power Series Solutions of AODEs - Existence, Uniqueness, Convergence and Computation

S. Falkensteiner

RISC Hagenberg, Johannes Kepler University Linz. PhD Thesis. June 2020. Also available as RISC report no. 20-13. [pdf]

[bib]

@phdthesis{RISC6120,
author = {S. Falkensteiner},
title = {{Power Series Solutions of AODEs - Existence, Uniqueness, Convergence and Computation}},
language = {english},
year = {2020},
month = {June},
note = {Also available as RISC report no. 20-13},
translation = {0},
school = {RISC Hagenberg, Johannes Kepler University Linz},
length = {146}
}

[Falkensteiner]

Algebraic, Rational and Puiseux Series Solutions of Systems of Autonomous Algebraic ODEs of Dimension One

J. Cano, S. Falkensteiner, R. Sendra

Mathematics in Computer Science 15, pp. 189-198. 2020. ISSN 16618289. [doi]

[bib]

@article{RISC6261,
author = {J. Cano and S. Falkensteiner and R. Sendra},
title = {{Algebraic, Rational and Puiseux Series Solutions of Systems of Autonomous Algebraic ODEs of Dimension One}},
language = {english},
journal = {Mathematics in Computer Science},
volume = {15},
pages = {189--198},
isbn_issn = {ISSN 16618289},
year = {2020},
refereed = {yes},
keywords = {Algebraic autonomous ordinary differential equation, Formal Puiseux series solution, Algebraic solutions, Rational solutions, Convergent solution, Algebraic space curve},
length = {10},
url = {https://doi.org/10.1007/s11786-020-00478-w}
}

[Falkensteiner]

The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry

S. Falkensteiner, C. Garay-Lopez, M. Haiech, M. P. Noordman, Z. Toghani, F. Boulier

In: ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, Angelos Mantzaflaris (ed.), Proceedings of 45th International Symposium on Symbolic and Algebraic Computation (ISSAC), pp. 178-185. 07 2020. Association for Computing Machinery, ISBN 9781450371001.

[bib]

@inproceedings{RISC6263,
author = {S. Falkensteiner and C. Garay-Lopez and M. Haiech and M. P. Noordman and Z. Toghani and F. Boulier},
title = {{The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry}},
booktitle = {{ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation}},
language = {english},
pages = {178--185},
publisher = {Association for Computing Machinery},
isbn_issn = {ISBN 9781450371001},
year = {2020},
month = {07},
annote = {Distinguished Paper Award},
editor = {Angelos Mantzaflaris},
refereed = {yes},
keywords = {Differential Algebra, Power series solutions, Arc spaces, Newton Polytope, Tropical Differential Algebraic Geometry},
length = {8},
conferencename = {45th International Symposium on Symbolic and Algebraic Computation (ISSAC)}
}

2019

[Falkensteiner]

Solving First Order Autonomous Algebraic Ordinary Differential Equations by Places

S. Falkensteiner, R. Sendra

Mathematics in Computer Science 14, pp. 327-337. 12 2019. ISSN 1661-8289. [doi]

[bib]

@article{RISC6035,
author = {S. Falkensteiner and R. Sendra},
title = {{Solving First Order Autonomous Algebraic Ordinary Differential Equations by Places}},
language = {english},
journal = {Mathematics in Computer Science},
volume = {14},
pages = {327--337},
isbn_issn = {ISSN 1661-8289},
year = {2019},
month = {12},
refereed = {yes},
keywords = {Algebraic autonomous differential equation, Algebraic curve, Local parametrization, Place, Formal power series solution, Analytic solution},
length = {11},
url = {https://doi.org/10.1007/s11786-019-00431-6}
}