Reproducibility and the Concept of Numerical Solution

Lenhard J, Kuester U. Reproducibility and the Concept of Numerical Solution. MINDS AND MACHINES. 2019;29(1):19-36.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)