000 03830nam a22005775i 4500
001 978-3-319-32726-6
003 DE-He213
005 20220201124707.0
007 cr nn 008mamaa
008 160615s2016 sz | s |||| 0|eng d
020 _a9783319327266
_9978-3-319-32726-6
024 7 _a10.1007/978-3-319-32726-6
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.35
_223
100 1 _aLangtangen, Hans Petter.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aScaling of Differential Equations
_h[electronic resource] /
_cby Hans Petter Langtangen, Geir K. Pedersen.
250 _a1st ed. 2016.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXIII, 138 p. 22 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSimula SpringerBriefs on Computing,
_x2512-1685 ;
_v2
505 0 _aPreface -- 1 Dimensions and Units -- 2 Ordinary Differential Equations Models -- 3 Basic Partial Differential Equations Models -- Advanced Partial Differential Equations Models -- References -- Index.
506 0 _aOpen Access
520 _aThe 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.
650 0 _aDifferential equations.
650 0 _aMathematical models.
650 0 _aMathematics—Data processing.
650 0 _aComputer simulation.
650 1 4 _aDifferential Equations.
650 2 4 _aMathematical Modeling and Industrial Mathematics.
650 2 4 _aComputational Science and Engineering.
650 2 4 _aComputer Modelling.
700 1 _aPedersen, Geir K.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319327259
776 0 8 _iPrinted edition:
_z9783319327273
830 0 _aSimula SpringerBriefs on Computing,
_x2512-1685 ;
_v2
856 4 0 _uhttps://doi.org/10.1007/978-3-319-32726-6
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-SOB
999 _c444244
_d444244