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Symbolic Solutions of First-Order Algebraic ODEs

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Computer Algebra and Polynomials

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8942))

Abstract

Algebraic ordinary differential equations are described by polynomial relations between the unknown function and its derivatives. There are no general solution methods available for such differential equations. However, if the hypersurface determined by the defining polynomial of an algebraic ordinary differential equation admits a parametrization, then solutions can be computed and the solvability in certain function classes may be decided. After an overview of methods developed in the last decade we present a new and rather general method for solving algebraic ordinary differential equations.

G. Grasegger was supported by the Austrian Science Fund (FWF): W1214-N15, project DK11.

F. Winkler was partially supported by the Spanish Ministerio de Economía y Competitividad under the project MTM2011-25816-C02-01.

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Author information

Authors and Affiliations

  1. Doctoral Program Computational Mathematics, Research Institute for Symbolic Computation, Johannes Kepler University Linz, 4040, Linz, Austria

    Georg Grasegger

  2. Research Institute for Symbolic Computation, Johannes Kepler University Linz, 4040, Linz, Austria

    Franz Winkler

Authors
  1. Georg Grasegger
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  2. Franz Winkler
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Correspondence to Franz Winkler .

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Editors and Affiliations

  1. University of Cantabria, Santander, Spain

    Jaime Gutierrez

  2. Ricam Linz, Linz, Austria

    Josef Schicho

  3. University of Caen, Caen, France

    Martin Weimann

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Grasegger, G., Winkler, F. (2015). Symbolic Solutions of First-Order Algebraic ODEs. In: Gutierrez, J., Schicho, J., Weimann, M. (eds) Computer Algebra and Polynomials. Lecture Notes in Computer Science(), vol 8942. Springer, Cham. https://doi.org/10.1007/978-3-319-15081-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-15081-9_5

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  • Online ISBN: 978-3-319-15081-9

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