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Scaling of Differential Equations
Hans Petter Langtangen and Geir K. Pedersen
2016
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.
This book is included in DOAB.
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- 150 - pdf (CC BY-NC) at OAPEN Library.
- 167 - pdf (CC BY-NC) at Unglue.it.
Keywords
- Analysis
- applied mathematics
- Calculus & mathematical analysis
- Computational Science and Engineering
- Computer modelling & simulation
- Computer science
- Computing & information technology
- Differential calculus & equations
- Differential equations
- dimensionless numbers
- fluid mechanics
- Mathematical Modeling and Industrial Mathematics
- mathematical modelling
- Mathematics
- Mathematics & science
- Maths for engineers
- Maths for scientists
- multiphysics models
- non-dimensionalization
- ordinary differential equations
- Partial Differential equations
- scaling
- Science: general issues
- Simulation and Modeling
- thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations
- thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWH Mathematical modelling
- thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists
- thema EDItEUR::U Computing and Information Technology::UY Computer science::UYM Computer modelling and simulation
Links
DOI: 10.1007/978-3-319-32726-6web: https://link.springer.com/book/10.1007/978-3-319-32726-6
Editions
