Symbolic Solutions of Algebraic Differential Equations [ADE-solve]
Project Lead
Project Duration
01/05/2018 - 31/05/2021
Partners
The Austrian Science Fund (FWF)
Software
AGADE
A Maple package for computing rational general solutions of first-order algebraic ODEs
The Maple package AGADE implements several methods for computing rational general solutions of first-order algebraic ordinary differential equations and planar rational systems. An advantage of these methods, compared to the standard dsolve-routine in Maple, is that the implemented algorithms provide ...
Authors: Johann Mitteramskogler
MoreSoftware WebsitePublications
2023
[Mitteramskogler]
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.@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}
}
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]@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}
}
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}
}
2021
[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]@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}
}
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}
}
[Sendra]
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]@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}
}
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}
}
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]@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}
}
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}
}
[Mitteramskogler]
A comparison of methods for computing rational general solutions of algebraic ODEs
Johann J. Mitteramskogler, Franz Winkler
Technical report no. 20-11 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). 2020. [pdf]@techreport{RISC6135,
author = {Johann J. Mitteramskogler and Franz Winkler},
title = {{A comparison of methods for computing rational general solutions of algebraic ODEs}},
language = {english},
number = {20-11},
year = {2020},
length = {21},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
author = {Johann J. Mitteramskogler and Franz Winkler},
title = {{A comparison of methods for computing rational general solutions of algebraic ODEs}},
language = {english},
number = {20-11},
year = {2020},
length = {21},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
[Sendra]
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]@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}
}
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}
}
2019
[Sendra]
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]@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}
}
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}
}
2018
[Vo]
Computation of all rational solutions of first-order algebraic ODEs
N.T. Vo, G. Grasegger, F. Winkler
Advances in Applied Mathematics 98, pp. 1-24. March 2018. Elsevier, 0196-8858. [doi]@article{RISC5797,
author = {N.T. Vo and G. Grasegger and F. Winkler},
title = {{Computation of all rational solutions of first-order algebraic ODEs}},
language = {english},
journal = {Advances in Applied Mathematics},
volume = {98},
pages = {1--24},
publisher = {Elsevier},
isbn_issn = {0196-8858},
year = {2018},
month = {March},
refereed = {yes},
keywords = {Ordinary differential equation, Rational solution, Algebraic function field, Rational curve},
length = {24},
url = {https://doi.org/10.1016/j.aam.2018.03.002}
}
author = {N.T. Vo and G. Grasegger and F. Winkler},
title = {{Computation of all rational solutions of first-order algebraic ODEs}},
language = {english},
journal = {Advances in Applied Mathematics},
volume = {98},
pages = {1--24},
publisher = {Elsevier},
isbn_issn = {0196-8858},
year = {2018},
month = {March},
refereed = {yes},
keywords = {Ordinary differential equation, Rational solution, Algebraic function field, Rational curve},
length = {24},
url = {https://doi.org/10.1016/j.aam.2018.03.002}
}
