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On the presumed superiority of analytical solutions over numerical methods

  • Vincent ArdourelEmail author
  • Julie Jebeile
Original Paper in Philosophy of Science

Abstract

An important task in mathematical sciences is to make quantitative predictions, which is often done via the solution of differential equations. In this paper, we investigate why, to perform this task, scientists sometimes choose to use numerical methods instead of analytical solutions. Via several examples, we argue that the choice for numerical methods can be explained by the fact that, while making quantitative predictions seems at first glance to be facilitated by analytical solutions, this is actually often much easier with numerical methods. Thus we challenge the widely presumed superiority of analytical solutions over numerical methods.

Keywords

Applied mathematics Exactness Analytical solutions Numerical methods 

Notes

Acknowledgments

We thank the anonymous reviewers for their helpful comments, and their contribution to enhancing the quality of this paper. This work was supported by French State funds managed by the National Research Agency on the behalf of Idex Sorbonne Universités within the Investissements d’Avenir Programme under reference ANR-11-IDEX-0004-02. One of the authors is currently a beneficiary of a “MOVE-IN Louvain” Incoming Post-doctoral Fellowship, co-funded by the Marie Curie Actions of the European Commission.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Institut Supérieur de PhilosophieUniversité catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Sciences, Normes, Décision (FRE 3593 CNRS, Université Paris-Sorbonne)ParisFrance

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