TY - BOOK ID - 7765073 TI - Scaling of Differential Equations AU - Langtangen, Hans Petter. AU - Pedersen, Geir K. PY - 2016 SN - 3319327259 3319327267 PB - Cham Springer Nature DB - UniCat KW - Mathematics. KW - Computer simulation. KW - Differential equations. KW - Partial differential equations. KW - Computer mathematics. KW - Mathematical models. KW - Ordinary Differential Equations. KW - Partial Differential Equations. KW - Mathematical Modeling and Industrial Mathematics. KW - Computational Science and Engineering. KW - Simulation and Modeling. KW - Math KW - Models, Mathematical KW - Computer mathematics KW - Discrete mathematics KW - Electronic data processing KW - Partial differential equations KW - 517.91 Differential equations KW - Differential equations KW - Computer modeling KW - Computer models KW - Modeling, Computer KW - Models, Computer KW - Simulation, Computer KW - Mathematics KW - Science KW - Simulation methods KW - Electromechanical analogies KW - Mathematical models KW - Model-integrated computing KW - Differential Equations. KW - Differential equations, partial. KW - Computer science. KW - Informatics KW - Simulation and modeling UR - https://www.unicat.be/uniCat?func=search&query=sysid:7765073 AB - The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations. ER -