European Journal for Philosophy of Science 7 (2):201-220 (2017)
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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.
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Keywords | Applied mathematics Exactness Analytical solutions Numerical methods |
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DOI | 10.1007/s13194-016-0152-2 |
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References found in this work BETA
Extending Ourselves: Computational Science, Empiricism, and Scientific Method.Paul Humphreys - 2004 - Oxford University Press.
The Philosophical Novelty of Computer Simulation Methods.Paul Humphreys - 2009 - Synthese 169 (3):615 - 626.
Models, Measurement and Computer Simulation: The Changing Face of Experimentation.Margaret Morrison - 2009 - Philosophical Studies 143 (1):33-57.
Computer Simulations as Experiments.Anouk Barberousse, Sara Franceschelli & Cyrille Imbert - 2009 - Synthese 169 (3):557 - 574.
The World as a Process: Simulations in the Natural and Social Sciences.Stephan Hartmann - 1996 - In Rainer Hegselmann (ed.), Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View.
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Citations of this work BETA
Computer Simulations in Science and Engineering. Concept, Practices, Perspectives.Juan Manuel Durán - 2018 - Springer.
Concepts of Solution and the Finite Element Method: A Philosophical Take on Variational Crimes.Nicolas Fillion & Robert M. Corless - 2021 - Philosophy and Technology 34 (1):129-148.
A Formal Framework for Computer Simulations: Surveying the Historical Record and Finding Their Philosophical Roots.Juan M. Durán - 2021 - Philosophy and Technology 34 (1):105-127.
A Formal Framework for Computer Simulations: Surveying the Historical Record and Finding Their Philosophical Roots.Juan M. Durán - 2021 - Philosophy and Technology 34 (1):105-127.
Numerical Instability and Dynamical Systems.Vincent Ardourel & Julie Jebeile - 2021 - European Journal for Philosophy of Science 11 (2):1-21.
View all 7 citations / Add more citations
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