The Vindication of Computer Simulations

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.