On the presumed superiority of analytical solutions over numerical methods

Ardourel, Vincent; Jebeile, Julie

doi:10.1007/s13194-016-0152-2

Cited by 17 publications

(8 citation statements)

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“…We will have more to say about this throughout this book. 2 Finally, tackling problems in computer simulations can be very different depending on the viewpoint adopted. For the problem-solving viewpoint, any issues related to the results of the simulation (e.g., accuracy, computability, representability, etc.)…”

Section: What Are Computer Simulations?mentioning

confidence: 99%

“…To illustrate some of the points made so far, take a simple equation-based computer simulation of the dynamics of satellite orbiting around a planet under tidal stress. To simulate such dynamics, researchers typically begins with a mathematical model of 2 Many philosophers have tried to understand the nature of computer simulations. What I have offered above is just one possible characterization.…”

Section: What Are Computer Simulations?mentioning

confidence: 99%

“…[and] analytical methods do not offer a generic approach for solving equations like [computer simulations do]" 7 [2,203]. Now, advocates of the problem-solving viewpoint are also present in contemporary literature.…”

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Computer simulations in science and engineering - Concepts - Practices - Perspectives

Durán

2019

Preprint

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is another member of this group, but he deserves special recognition. Andrés read every chapter of the book, made thoughtful comments, and amended several mistakes that had gone unnoticed by me. He has also diligently checked many of the formulas I use in the book. For this and for the innumerable discussions we have had, thank you Andy. Naturally, all mistakes are my responsibility. A very sincere thanks goes to CIFFyH, the UNC, and CONICET, for their support to the Humanities in general and to me in particular.I also have many people to thank that, although they did not contribute directly to the book, they showed their support and encouragement throughout good and bad days. My eternal gratitude goes to my good friend Mauricio Zalazar, and my sister Jo. Thank you guys for being there when I need you the most. My parents have also been a constant source of support and love, thank you mom and dad, this book would not exist without you. Thanks also go to Víctor Scarafía and my newly adopted family: the Pompers & the Ebers. Thank you all guys for being so great. Special thanks go the the two Omas: Oma Pomper and Oma Eber. I love you ladies. Finally, thanks go to Peter Ostritsch for his support in many aspect of my life, most of them unrelated to this book.The book ended at the Department of Philosophy of Science and Technology of Computer Simulation, at the High-Performance Computing Center Stuttgart (HLRS), University of Stuttgart. The department was created by Michael Resch and Andreas Kaminski and funded by the Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg (MWK), whom I thank for providing a comfortable atmosphere for working on the book. I extend my thanks to all the members of the department, Nico Formanek, Michael Hermann, Alena Wackerbarth, and Hildrun Lampe, I will never forget the many fundamental philosophical discussions we had at lunch -and over our new espresso machine -on the most varied of topics. I feel especially lucky to share an office with Nico and Michael, good friends and great philosophers. Thank you guys for checking the formulas that I included in the book. The mistakes are, again, entirely my responsibility. Thanks also go to Björn Schembera, a true philosopher in disguise, for our time discussing so many technical issues about computer simulations, some of which found a place in the book. From the visualization department at the HLRS, thanks go to Martin Aumüller, Thomas Obst, Wolfgang Schotte, and Uwe Woessner who patiently explained to me the many details of their work as well as provided the

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Section: What Are Computer Simulations?mentioning

confidence: 99%

Section: What Are Computer Simulations?mentioning

confidence: 99%

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Computer simulations in science and engineering - Concepts - Practices - Perspectives

Durán

2019

Preprint

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“…There are, however, cases where the use of numerical solutions is preferred although scientists know the exact solutions(Ardourel and Jebeile 2017).12 We are in debt to an anonymous reviewer for providing such insights.…”

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confidence: 99%

Numerical instability and dynamical systems

Ardourel

Jebeile

2021

Euro Jnl Phil Sci

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In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of numerical methods involving a discretization process, where discretization is required to solve the differential equations of dynamical systems on a computer. We argue that the criteria for numerical stability, as usually provided by numerical analysis textbooks, are insufficient, and, after mentioning the promising development of backward analysis, we discuss to what extent, in practice, numerical instability can be controlled or avoided.

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“…In a recent article,Ardourel and Jebeile (2017) question the supposed superiority of analytic solutions over numerical solutions' characteristic of computer simulations. 10 In his own words, "[i]n order to solve at least some of these problems [the present geography of the strata, the strong theory ladenness of the interpreted data, the complex interdependencies within geological systems, and so on], geologists have devised simulation techniques like STRATAGEM [...]"(Guala 2002, 68; Emphasis in original).…”

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A Formal Framework for Computer Simulations: Surveying the Historical Record and Finding Their Philosophical Roots

Durán

2019

Philos. Technol.

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A chronicled approach to the notion of computer simulations shows that there are two predominant interpretations in the specialized literature. According to the first interpretation, computer simulations are techniques for finding the set of solutions to a mathematical model. I call this first interpretation the problem-solving technique viewpoint (PST). In its second interpretation, computer simulations are considered to describe patterns of behavior of a target system. I call this second interpretation the description of patterns of behavior viewpoint of computer simulations (DPB). This article explores these two interpretations of computer simulations from three different angles. First, I collect a series of definitions of computer simulation from the historical record. I track back definitions to the early 1960s and show how each viewpoint shares similar interpretations of computer simulations-ultimately clustering into the two viewpoints aforementioned. This reconstruction also includes the most recent literature. Second, I unpack the philosophical assumptions behind each viewpoint, with a special emphasis on their differences. Third, I discuss the philosophical implications of each viewpoint in the context of the recent discussion on the logic of scientific explanation for computer simulations.Keywords History and philosophy of computer simulations . Two viewpoints on computer simulations . Problem-solving techniques viewpoint . Description of patterns of behavior viewpoint . Scientific explanation Philosophy & Technology

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On the presumed superiority of analytical solutions over numerical methods

Cited by 17 publications

References 30 publications

Computer simulations in science and engineering - Concepts - Practices - Perspectives

Computer simulations in science and engineering - Concepts - Practices - Perspectives

Numerical instability and dynamical systems

A Formal Framework for Computer Simulations: Surveying the Historical Record and Finding Their Philosophical Roots

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