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Symbolic-Numeric Methods for Nonlinear Integro-Differential Modeling

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Computer Algebra in Scientific Computing (CASC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11077))

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Abstract

This paper presents a proof of concept for symbolic and numeric methods dedicated to the parameter estimation problem for models formulated by means of nonlinear integro-differential equations (IDE). In particular, we address: the computation of the model input-output equation and the numerical integration of IDE systems.

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Notes

  1. 1.

    Butcher tableaux were introduced by Butcher in [16] to provide a compact description of “Runge-Kutta methods”. To each tableau is associated a number of stages (customarily denoted s) and an order (customarily denoted p). The computational cost of a Runge-Kutta method increases with the number of stages. The efficiency increases with the order. The coefficients of the tableaux are denoted \(c_i\) (the leftmost column), \(b_j\) (the bottom row) and \(a_{i,j}\) (the matrix).

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Acknowledgment

This work has been supported by the bilateral project ANR-17-CE40-0036 and DFG-391322026 SYMBIONT.

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Authors and Affiliations

  1. Univ. Lille, CNRS, Centrale Lille, Inria, UMR 9189 - CRIStAL - Centre de Recherche en Informatique Signal et Automatique de Lille, 59000, Lille, France

    François Boulier, François Lemaire, Adrien Poteaux & Alban Quadrat

  2. Normandie Univ, France, UNIHAVRE, LMAH, FR CNRS 3335, ISCN, 76600, Le Havre, France

    Nathalie Corson, Valentina Lanza & Nathalie Verdière

  3. INSERM, DC2N, Normandie Univ, UNIROUEN, 76000, Rouen, France

    Hélène Castel

Authors
  1. François Boulier
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  2. Hélène Castel
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  3. Nathalie Corson
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  4. Valentina Lanza
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  5. François Lemaire
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  6. Adrien Poteaux
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  7. Alban Quadrat
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  8. Nathalie Verdière
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Correspondence to François Boulier .

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Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Werner M. Seiler

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Boulier, F. et al. (2018). Symbolic-Numeric Methods for Nonlinear Integro-Differential Modeling. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2018. Lecture Notes in Computer Science(), vol 11077. Springer, Cham. https://doi.org/10.1007/978-3-319-99639-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-99639-4_6

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