Computability of Differential Equations

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Abstract

In this chapter, we provide a survey of results concerning the computability and computational complexity of differential equations. In particular, we study the conditions which ensure computability of the solution to an initial value problem for an ordinary differential equation (ODE) and analyze the computational complexity of a computable solution. We also present computability results concerning the asymptotic behaviors of ODEs as well as several classically important partial differential equations.

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Authors and Affiliations

  1. Universidade do Algarve, Faro, Portugal

    Daniel S. GraÇa

  2. Instituto de TelecomunicaÇões, Faro, Portugal

    Daniel S. GraÇa

  3. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio, USA

    Ning Zhong

Authors

  1. Daniel S. GraÇa
  2. Ning Zhong

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Correspondence to Daniel S. GraÇa .

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Editors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, South Africa

    Vasco Brattka

  2. Fakultät für Informatik, Universität der Bundeswehr München, Neubiberg, Germany

    Peter Hertling

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GraÇa, D.S., Zhong, N. (2021). Computability of Differential Equations. In: Brattka, V., Hertling, P. (eds) Handbook of Computability and Complexity in Analysis. Theory and Applications of Computability. Springer, Cham. https://doi.org/10.1007/978-3-030-59234-9_3

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  • DOI: https://doi.org/10.1007/978-3-030-59234-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59233-2

  • Online ISBN: 978-3-030-59234-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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