Modeling and simulation are used in a myriad of ways in business and government. The range covers science, engineering and technology, industry, environmental regulations and safety, product and plant safety, financial investing, design of military systems, governmental planning, and many more. In all of these activities models are built that are mental constructs of how we believe the activity functions and how it is influenced by events or surroundings. All models are abstractions of the real activity that are based on many different types of approximation. These models are then programmed for execution on a digital computer, and the computer produces a simulation result. The simulation result may have high fidelity to the actual activity of interest, or it may be complete nonsense. The question is: how can we tell which is which? This book deals with various technical and procedural tools that can be used to assess the fidelity of modeling and simulation aspects of scientific computing. Our focus is on physical processes and systems in a broad range of the natural sciences and engineering.

The tools discussed here are primarily focused on mathematical models that are represented by differential and/or integral equations. Many of these mathematical models occur in physics, chemistry, astronomy, Earth sciences, and engineering, but they also occur in other fields of modeling and simulation. The topics addressed in this book are all related to the principles involved in assessing the credibility of the models and the simulation results. We do not deal with the specific details of modeling the physical process or system of interest, but with assessment procedures relating to the fidelity of the models and simulations. These procedures are typically described by the terms verification and validation.