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2017 | OriginalPaper | Buchkapitel

The Vindication of Computer Simulations

verfasst von : Nicolas Fillion

Erschienen in: Mathematics as a Tool

Verlag: Springer International Publishing

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Abstract

The relatively recent increase in prominence of computer simulations in scientific inquiry gives us more reasons than ever before for asserting that mathematics is a wonderful tool. In fact, a practical knowledge (a ‘know-how’) of scientific computation has become essential for scientists working in all disciplines involving mathematics. Despite their incontestable success, it must be emphasized that the numerical methods subtending simulations provide at best approximate solutions and that they can also return very misleading results. Accordingly, epistemological sobriety demands that we clarify the circumstances under which simulations can be relied upon. With this in mind, this paper articulates a general perspective to better understand and compare the strengths and weaknesses of various error-analysis methods.

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For more details on the relation between the unreasonable effectiveness of mathematics and computational issues, see Fillion (2012).

Note however that despite the broad use of this terminology in computational mechanics, it remains comparatively rare in the field of numerical analysis.

For an excellent discussion of such complications, see Borwein and Crandall (2010). For a more philosophical discussion, see Fillion and Bangu (2015).

See also, e.g., Feigl (1950) and Salmon (1991).

For a similar claim, see Grcar (2011). For a more extensive explication of the notions introduced below, see Corless and Fillion (2013). Higham (2002) and Deuflhard and Hohmann (2003) are also excellent alternative presentations.

For more details on this, see Fillion and Corless (2014).

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Titel: The Vindication of Computer Simulations
verfasst von: Nicolas Fillion
Verlag: Springer International Publishing
Buch: Mathematics as a Tool
Print ISBN: 978-3-319-54468-7

Electronic ISBN: 978-3-319-54469-4

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-54469-4_8