新生學校財團法人新生醫護管理專科學校圖書館 |

Numerical time-dependent partial differential equations for scientists and engineers

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical time-dependent partial differential equations for scientists and engineers/ Moysey Brio, Aramais R. Zakharian, Gary M. Webb.
Author:	Brio, Moysey,
other author:	Webb, Gary M.
Published:	Amsterdam ;Elsevier, : 2010.,
Description:	1 online resource (x, 294 p.) :ill. :
Subject:	Differential equations, Partial - Numerical solutions. -
Online resource:	http://www.sciencedirect.com/science/book/9780121339814
ISBN:	9780080917047 (electronic bk.)

Numerical time-dependent partial differential equations for scientists and engineers
Brio, Moysey,1952-

Numerical time-dependent partial differential equations for scientists and engineers[electronic resource] /Moysey Brio, Aramais R. Zakharian, Gary M. Webb. - 1st ed. - Amsterdam ;Elsevier,2010. - 1 online resource (x, 294 p.) :ill. - Mathematics in science and engineering,v. 2130076-5392 ;. - Mathematics in science and engineering ;v. 189..

Includes bibliographical references (p. 273-287) and index.

Overview of properties partial differential equations -- Methods of discretization -- Convergence theory for initial value problems -- Numerical boundary conditions -- Problems with multiple temporal and spatial scales -- Nonuniform, adaptive and moving grids.

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations.

ISBN: 9780080917047 (electronic bk.)

Source: 89633:89633Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

122837
Differential equations, Partial
--Numerical solutions.Index Terms--Genre/Form:

96803
Electronic books.

LC Class. No.: QA377 / .B75 2010

Dewey Class. No.: 515.353

Numerical time-dependent partial differential equations for scientists and engineers
LDR:04687cmm 2200433Ia 4500 001 166800
003 OCoLC
005 20111122091028.0
006 m d
007 cr mn|||||||||
008 160302s2010 ne a ob 001 0 eng d
020 $a 9780080917047 (electronic bk.)
020 $a 0080917046 (electronic bk.)
020 $z 9780121339814
020 $z 0121339815
029 1 $a NZ1 $b 13642331
029 1 $a AU@ $b 000047499799
035 $a (OCoLC)668208508
035 $a ocn668208508
037 $a 89633:89633 $b Elsevier Science & Technology $n http://www.sciencedirect.com
040 $a OPELS $b eng $c OPELS $d OSU $d E7B $d EBLCP $d OCLCQ $d CDX $d YDXCP $d OPELS
049 $a TEFA
050 4 $a QA377 $b .B75 2010
082 0 4 $a 515.353 $2 22
100 1 $a Brio, Moysey, $d 1952- $3 324626
245 1 0 $a Numerical time-dependent partial differential equations for scientists and engineers $h [electronic resource] / $c Moysey Brio, Aramais R. Zakharian, Gary M. Webb.
250 $a 1st ed.
260 $a Amsterdam ; $a Boston : $c 2010. $b Elsevier,
300 $a 1 online resource (x, 294 p.) : $b ill.
490 1 $a Mathematics in science and engineering, $x 0076-5392 ; $v v. 213
504 $a Includes bibliographical references (p. 273-287) and index.
505 0 $a Overview of properties partial differential equations -- Methods of discretization -- Convergence theory for initial value problems -- Numerical boundary conditions -- Problems with multiple temporal and spatial scales -- Nonuniform, adaptive and moving grids.
520 $a It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations.
588 $a Description based on print version record.
650 0 $a Differential equations, Partial $x Numerical solutions. $3 122837
650 4 $a Mathematics. $3 83487
655 4 $a Electronic books. $2 local. $3 96803
700 1 $a Webb, Gary M. $3 324627
700 1 $a Zakharian, Aramais R. $3 324628
776 0 8 $i Print version: $a Brio, Moysey, 1952- $t Numerical time-dependent partial differential equations for scientists and engineers. $b 1st ed. $d Amsterdam [Netherlands] ; Boston [i.e. Burlington, MA] : Elsevier, 2010 $z 9780121339814 $w (OCoLC)645697653
830 0 $a Mathematics in science and engineering ; $v v. 189. $3 257499
856 4 0 $3 ScienceDirect $u http://www.sciencedirect.com/science/book/9780121339814
938 $a ebrary $b EBRY $n ebr10415252
938 $a EBL - Ebook Library $b EBLB $n EBL648517
938 $a Coutts Information Services $b COUT $n 15337535
938 $a YBP Library Services $b YANK $n 3467488
994 $a C0 $b TEF