Minds and Machines

, Volume 29, Issue 1, pp 19–36 | Cite as

Reproducibility and the Concept of Numerical Solution

  • Johannes LenhardEmail author
  • Uwe Küster


In this paper, we show that reproducibility is a severe problem that concerns simulation models. The reproducibility problem challenges the concept of numerical solution and hence the conception of what a simulation actually does. We provide an expanded picture of simulation that makes visible those steps of simulation modeling that are numerically relevant, but often escape notice in accounts of simulation. Examining these steps and analyzing a number of pertinent examples, we argue that numerical solutions are importantly different from usual mathematical solutions. They are do not merely approximate the latter, but introduce new problems, including issues of artificiality, stability, and well-posedness. Consequently, simulation modelling can attain reproducibility only to a certain degree because it is working with numerical solutions (in a sense we specify in the paper).


Artificiality Ill-posed problems Mathematical solution Numerical solution Reproducibility Stability Tractability 



We like to thank three anonymous reviewers for useful suggestions and Nicholas Danne for his support in approximating our text to English language.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Philosophy of Science and Technology of Computer Simulation, High Performance Computing CenterUniversity of StuttgartStuttgartGermany
  2. 2.Department for Numerics and Libraries, High Performance Computing CenterUniversity of StuttgartStuttgartGermany
  3. 3.Department of PhilosophyBielefeld UniversityBielefeldGermany

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