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Computational Complexity of Classical Solutions of Partial Differential Equations

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Revolutions and Revelations in Computability (CiE 2022)

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Abstract

This paper provides a brief survey of recent achievements in characterizing computational complexity of partial differential equations (PDEs), as well as computing solutions with guaranteed precision within the exact real computation approach. The emphasis is on classical solutions and linear PDE systems, since these are the cases where most of the progress has been achieved so far. Complexity, as it turns out, heavily depends on the smoothness of the initial data, which has similarities with the situation for ordinary differential equations (ODEs).

Supported by the National Research Foundation of Korea (grant 2017R1E1A1A03071032) and by the International Research & Development Program of the Korean Ministry of Science and ICT (grant 2016K1A3A7A03950702) and by the NRF Brain Pool program (grant 2019H1D3A2A02102240) and by the RFBR-JSPS Grant 20-51-50001. The author is thankful to Victor Selivanov, Holger Thies and Martin Ziegler for valuable discussions.

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Authors and Affiliations

  1. KAIST, School of Computing, Daejeon, Republic of Korea

    Svetlana Selivanova

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  1. Svetlana Selivanova
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Correspondence to Svetlana Selivanova .

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Editors and Affiliations

  1. Department of Computer Science, Swansea University, Swansea, UK

    Ulrich Berger

  2. Department of Mathematics, Hofstra University, Hempstead, NY, USA

    Johanna N. Y. Franklin

  3. Georg-August University Göttingen, Göttingen, Germany

    Florin Manea

  4. Department of Computer Science, Swansea University, Swansea, UK

    Arno Pauly

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Selivanova, S. (2022). Computational Complexity of Classical Solutions of Partial Differential Equations. In: Berger, U., Franklin, J.N.Y., Manea, F., Pauly, A. (eds) Revolutions and Revelations in Computability. CiE 2022. Lecture Notes in Computer Science, vol 13359. Springer, Cham. https://doi.org/10.1007/978-3-031-08740-0_25

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  • DOI: https://doi.org/10.1007/978-3-031-08740-0_25

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