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Transforming ODEs and PDEs from Radical Coefficients to Rational Coefficients

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Abstract

We present an algorithm that transforms, if possible, a given ODE or PDE with radical function coefficients into one with rational coefficients by means of a rational change of variables so that solutions correspond one-to-one. Our method also applies to systems of linear ODEs. It is based on previous work on reparametrization of radical algebraic varieties.

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Authors and Affiliations

  1. Department of Physics and Mathematics, University of Alcalá, 28871, Alcalá de Henares, Madrid, Spain

    Jorge Caravantes, J. Rafael Sendra & Carlos Villarino

  2. Department of Mathematics, University of Extremadura, Av. Santa Teresa de Jornet 38, 06800, Mérida, Badajoz, Spain

    David Sevilla

Authors
  1. Jorge Caravantes
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  2. J. Rafael Sendra
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  3. David Sevilla
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  4. Carlos Villarino
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Correspondence to David Sevilla.

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The authors are partially supported by FEDER/Ministerio de Ciencia, Innovación y Universidades—Agencia Estatal de Investigación/MTM2017-88796-P (Symbolic Computation: new challenges in Algebra and Geometry together with its applications).

Jorge Caravantes, J. Rafael Sendra and Carlos Villarino are members of the Research Group ASYNACS (Ref. CT-CE2019/683). In addition, J. Rafael Sendra is also partially supported by Dirección General de Investigación e Innovación, Consejería de Educación e Investigación of the Comunidad de Madrid (Spain), and Universidad de Alcalá (UAH) under grant CM/JIN/2019-010.

David Sevilla is a member of the research group GADAC and is partially supported by Junta de Extremadura and FEDER funds (group FQM024).

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Caravantes, J., Sendra, J.R., Sevilla, D. et al. Transforming ODEs and PDEs from Radical Coefficients to Rational Coefficients. Mediterr. J. Math. 18, 96 (2021). https://doi.org/10.1007/s00009-021-01703-x

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  • DOI: https://doi.org/10.1007/s00009-021-01703-x

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