rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Scaling of Differential Equations
  name:
    name part: Langtangen, Hans Petter.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Pedersen, Geir K.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 138 p. 22 illus. online resource.
  abstract: 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.
  table of contents: Preface -- 1 Dimensions and Units -- 2 Ordinary Differential Equations Models -- 3 Basic Partial Differential Equations Models -- Advanced Partial Differential Equations Models -- References -- Index.
  note: by Hans Petter Langtangen, Geir K. Pedersen.
  note: Open Access
  subject:
    topic: Mathematics
  subject:
    topic: Computer simulation
  subject:
    topic: Differential equations
  subject:
    topic: Partial differential equations
  subject:
    topic: Computer mathematics
  subject:
    topic: Mathematical models
  subject:
    topic: Mathematics
  subject:
    topic: Ordinary Differential Equations
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Mathematical Modeling and Industrial Mathematics
  subject:
    topic: Computational Science and Engineering
  subject:
    topic: Simulation and Modeling
  classification: QA372
  classification: 515.352
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Simula SpringerBriefs on Computing ; 2
  identifier: 9783319327266
  identifier: http://dx.doi.org/10.1007/978-3-319-32726-6
  access condition: Open Access
  record info:
    record creation date: 160615
    record change date: 20160615114059.0
    record identifier: 978-3-319-32726-6