大葉大學圖書館 |

Scaling of differential equations[electronic resource] /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	515.35
書名/作者:	Scaling of differential equations/ by Hans Petter Langtangen, Geir K. Pedersen.
作者:	Langtangen, Hans Petter.
其他作者:	Pedersen, Geir K.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	xiii, 138 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Differential equations - Numerical solutions.
標題:	Multiscale modeling.
標題:	Mathematics.
標題:	Ordinary Differential Equations.
標題:	Partial Differential Equations.
標題:	Mathematical Modeling and Industrial Mathematics.
標題:	Computational Science and Engineering.
標題:	Simulation and Modeling.
ISBN:	9783319327266
ISBN:	9783319327259
內容註:	Preface -- 1 Dimensions and Units -- 2 Ordinary Differential Equations Models -- 3 Basic Partial Differential Equations Models -- Advanced Partial Differential Equations Models -- References -- Index.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-32726-6

Scaling of differential equations[electronic resource] /
Langtangen, Hans Petter.

Scaling of differential equations[electronic resource] /by Hans Petter Langtangen, Geir K. Pedersen. - Cham :Springer International Publishing :2016. - xiii, 138 p. :ill., digital ;24 cm. - Simula SpringerBriefs on computing ;v.2. - Simula SpringerBriefs on computing ;v.1..

Preface -- 1 Dimensions and Units -- 2 Ordinary Differential Equations Models -- 3 Basic Partial Differential Equations Models -- Advanced Partial Differential Equations Models -- References -- Index.

Open access.

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.

ISBN: 9783319327266

Standard No.: 10.1007/978-3-319-32726-6doiSubjects--Topical Terms:

469413
Differential equations
--Numerical solutions.

LC Class. No.: QA371

Dewey Class. No.: 515.35

Scaling of differential equations[electronic resource] /
LDR:02743nmm a2200337 a 4500 001 458903
003 DE-He213
005 20161130114431.0
006 m d
007 cr nn 008maaau
008 170113s2016 gw s 0 eng d
020 $a 9783319327266 $q (electronic bk.)
020 $a 9783319327259 $q (paper)
024 7 $a 10.1007/978-3-319-32726-6 $2 doi
035 $a 978-3-319-32726-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA371
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
082 0 4 $a 515.35 $2 23
090 $a QA371 $b .L286 2016
100 1 $a Langtangen, Hans Petter. $3 590204
245 1 0 $a Scaling of differential equations $h [electronic resource] / $c by Hans Petter Langtangen, Geir K. Pedersen.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a xiii, 138 p. : $b ill., digital ; $c 24 cm.
490 1 $a Simula SpringerBriefs on computing ; $v v.2
505 0 $a Preface -- 1 Dimensions and Units -- 2 Ordinary Differential Equations Models -- 3 Basic Partial Differential Equations Models -- Advanced Partial Differential Equations Models -- References -- Index.
506 $a Open access.
520 $a 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.
650 0 $a Differential equations $x Numerical solutions. $3 469413
650 0 $a Multiscale modeling. $3 412280
650 1 4 $a Mathematics. $3 172349
650 2 4 $a Ordinary Differential Equations. $3 465742
650 2 4 $a Partial Differential Equations. $3 464931
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 463922
650 2 4 $a Computational Science and Engineering. $3 463702
650 2 4 $a Simulation and Modeling. $3 463796
700 1 $a Pedersen, Geir K. $3 660437
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a Simula SpringerBriefs on computing ; $v v.1. $3 639228
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-32726-6
950 $a Mathematics and Statistics (Springer-11649)