Linear Differential Equations as a Data Structure

Abstract

A lot of information concerning solutions of linear differential equations can be computed directly from the equation. It is therefore natural to consider these equations as a data structure, from which mathematical properties can be computed. A variety of algorithms has thus been designed in recent years that do not aim at “solving,” but at computing with this representation. Many of these results are surveyed here.

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Notes

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    Available at http://ddmf.msr-inria.inria.fr.

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    https://dlmf.nist.gov.

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Acknowledgements

This work has been supported in part by FastRelax ANR-14-CE25-0018-01.

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Salvy, B. Linear Differential Equations as a Data Structure. Found Comput Math 19, 1071–1112 (2019). https://doi.org/10.1007/s10208-018-09411-x

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Keywords

  • Computer algebra
  • Linear differential equations
  • Algorithms
  • Complexity

Mathematics Subject Classification

  • 68W30
  • 33F10