東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Numerical models for differential pr...

Quarteroni, Alfio.

FindBook

Google Book

Amazon

博客來

Numerical models for differential problems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Numerical models for differential problems/ by Alfio Quarteroni.
作者:	Quarteroni, Alfio.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	xvii, 681 p. :ill. (some col.), digital ;24 cm.
內容註:	1 A brief survey of partial differential equations -- 2 Elements of functional analysis -- 3 Elliptic equations -- 4 The Galerkin finite element method for elliptic problems -- 5 Parabolic equations -- 6 Generation of 1D and 2D grids -- 7 Algorithms for the solution of linear systems -- 8 Elements of finite element programming -- 9 The finite volume method -- 10 Spectral methods -- 11 Isogeometric analysis -- 12 Discontinuous element methods (D Gandmortar) -- 13 Diffusion-transport-reaction equations -- 14 Finite differences for hyperbolic equations -- 15 Finite elements and spectral methods for hyperbolic equations -- 16 Nonlinear hyperbolic problems -- 17 Navier-Stokes equations -- 18 Optimal control of partial differential equations -- 19 Domain decomposition methods -- 20 Reduced basis approximation for parametrized partial differential equations -- References.
Contained By:	Springer eBooks
標題:	Differential equations, Partial - Numerical solutions. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-49316-9
ISBN:	9783319493169

Numerical models for differential problems
Quarteroni, Alfio.

Numerical models for differential problems[electronic resource] /by Alfio Quarteroni. - 3rd ed. - Cham :Springer International Publishing :2017. - xvii, 681 p. :ill. (some col.), digital ;24 cm. - MS&A, modeling, simulation and applications,v.162037-5255 ;. - MS&A, modeling, simulation and applications ;v.16..

1 A brief survey of partial differential equations -- 2 Elements of functional analysis -- 3 Elliptic equations -- 4 The Galerkin finite element method for elliptic problems -- 5 Parabolic equations -- 6 Generation of 1D and 2D grids -- 7 Algorithms for the solution of linear systems -- 8 Elements of finite element programming -- 9 The finite volume method -- 10 Spectral methods -- 11 Isogeometric analysis -- 12 Discontinuous element methods (D Gandmortar) -- 13 Diffusion-transport-reaction equations -- 14 Finite differences for hyperbolic equations -- 15 Finite elements and spectral methods for hyperbolic equations -- 16 Nonlinear hyperbolic problems -- 17 Navier-Stokes equations -- 18 Optimal control of partial differential equations -- 19 Domain decomposition methods -- 20 Reduced basis approximation for parametrized partial differential equations -- References.

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

ISBN: 9783319493169

Standard No.: 10.1007/978-3-319-49316-9doiSubjects--Topical Terms:

540504
Differential equations, Partial
--Numerical solutions.

LC Class. No.: QA377 / .Q83 2017

Dewey Class. No.: 518.64

Numerical models for differential problems
LDR:03095nmm a2200337 a 4500 001 2111032
003 DE-He213
005 20180426153415.0
006 m d
007 cr nn 008maaau
008 180619s2017 gw s 0 eng d
020 $a 9783319493169 $q (electronic bk.)
020 $a 9783319493152 $q (paper)
024 7 $a 10.1007/978-3-319-49316-9 $2 doi
035 $a 978-3-319-49316-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377 $b .Q83 2017
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 518.64 $2 23
090 $a QA377 $b .Q1 2017
100 1 $a Quarteroni, Alfio. $3 628971
245 1 0 $a Numerical models for differential problems $h [electronic resource] / $c by Alfio Quarteroni.
250 $a 3rd ed.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2017.
300 $a xvii, 681 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a MS&A, modeling, simulation and applications, $x 2037-5255 ; $v v.16
505 0 $a 1 A brief survey of partial differential equations -- 2 Elements of functional analysis -- 3 Elliptic equations -- 4 The Galerkin finite element method for elliptic problems -- 5 Parabolic equations -- 6 Generation of 1D and 2D grids -- 7 Algorithms for the solution of linear systems -- 8 Elements of finite element programming -- 9 The finite volume method -- 10 Spectral methods -- 11 Isogeometric analysis -- 12 Discontinuous element methods (D Gandmortar) -- 13 Diffusion-transport-reaction equations -- 14 Finite differences for hyperbolic equations -- 15 Finite elements and spectral methods for hyperbolic equations -- 16 Nonlinear hyperbolic problems -- 17 Navier-Stokes equations -- 18 Optimal control of partial differential equations -- 19 Domain decomposition methods -- 20 Reduced basis approximation for parametrized partial differential equations -- References.
520 $a In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
650 0 $a Differential equations, Partial $x Numerical solutions. $3 540504
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Analysis. $3 891106
650 2 4 $a Numerical Analysis. $3 892626
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 891089
650 2 4 $a Applications of Mathematics. $3 890893
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a MS&A, modeling, simulation and applications ; $v v.16. $3 3264735
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-49316-9
950 $a Mathematics and Statistics (Springer-11649)