Scaling of differential equations [electronic resource] / Hans Petter Langtangen, Geir K. Pedersen.
Langtangen, Hans Petter, 1962- author.; Pedersen, Geir K. author.
2016
QA371
Available Online

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Title Scaling of differential equations [electronic resource] / Hans Petter Langtangen, Geir K. Pedersen.
Author Langtangen, Hans Petter, 1962- author.
ISBN 9783319327266 (electronic book)
3319327267 (electronic book)
9783319327259
DOI https://doi.org/10.1007/978-3-319-32726-6
Published Cham : Springer, 2016.
Language English
Description 1 online resource (xiii, 138 pages) : illustrations.
Item Number 10.1007/978-3-319-32726-6 doi
Call Number QA371
Dewey Decimal Classification 515/.35
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Open Access.
Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed June 29, 2016).
Added Author Pedersen, Geir K. author.
Series Simula SpringerBriefs on computing ; volume 2
Available in Other Form Print version: 9783319327259
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Record Appears in Online Resources > Ebooks
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Preface
1 Dimensions and Units
2 Ordinary Differential Equations Models
3 Basic Partial Differential Equations Models
Advanced Partial Differential Equations Models
References
Index.

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