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Discrete variational derivative meth...

Furihata, Daisuke.

Discrete variational derivative methoda structurepreserving numerical method for partial differential equations /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Discrete variational derivative methodDaisuke Furihata, Takayasu Matsuo.
其他題名:	a structurepreserving numerical method for partial differential equations /
作者:	Furihata, Daisuke.
其他作者:	Matsuo, Takayasu.
出版者:	Boca Raton, FL :Chapman and Hall/CRC,c2011.
面頁冊數:	1 online resource (xi, 376 p.) :ill.
標題:	Differential equations, PartialNumerical solutions.
電子資源:	http://www.crcnetbase.com/isbn/978-1-4200-9445-9

Discrete variational derivative methoda structurepreserving numerical method for partial differential equations /
Furihata, Daisuke.

Discrete variational derivative methoda structurepreserving numerical method for partial differential equations /[electronic resource] :Daisuke Furihata, Takayasu Matsuo. - Boca Raton, FL :Chapman and Hall/CRC,c2011. - 1 online resource (xi, 376 p.) :ill. - Chapman & Hall/CRC numerical analysis and scientific computing. - Chapman & Hall/CRC numerical analysis and scientific computing..

Includes bibliographical references and index.

1. Introduction and summary of this book An introductory example: the spinodal decomposition - History -- Derivation of dissipative or conservative schemes advanced topics -- 2. Target partial differential equations -- Variational derivatives -- First-order real-valued PDEs -- First-order complex-valued PDEs -- Systems of first-order PDEs -- Second-order PDEs -- 3. Discrete variational derivative method -- Discrete symbols and formulas -- Procedure for first-order real-valued PDEs -- Procedure for first-order complex-valued PDEs -- Procedure for systems of first-order PDEs -- Procedure for second-order PDEs -- Preliminaries on discrete functional analysis -- 4. Applications -- Target PDEs 1 -- Target PDEs 2 -- Target PDEs 3 -- Target PDEs 4 -- Target PDEs 5 -- Target PDEs 7 -- Other equations -- 5. Advanced topic I: design of high-order schemes -- Orders of accuracy of schemes -- Spatially high-order schemes -- Temporally high-order schemes: composition method -- Temporally high-order schemes: high-order discrete variational derivatives -- 6. Advanced topic II: design of linearly-implicit schemes -- Basic idea for constructing linearly-implicit schemes -- Multiple-points discrete variational derivative -- Design of schemes -- Applications -- Remarks on the stability of linearly-implicit schemes -- 7. Advanced topic III: further remarks -- Solving system of nonlinear equations -- Switch to Galerkin framework -- Extension to non-rectangular meshes on 2D Region -- A. Semi-discrete schemes in space B -- Proof of Proposition 3.4.

"Many important problems in engineering and science are modeled by nonlinear partial differential equations (PDEs). A new trend in PDEs, called structure-preserving numerical methods, has recently developed. This book is devoted to one such technique, called the discrete variational derivative method. First, the text introduces the key factors and the basic ideas of this method, followed by target problems solvable by the method. The second section describes the rigorous mathematics in detail along with relevant applications, which are illustrated by worked examples. It concludes with a comprehensive of listing of essential references on structure-preserving algorithms for advanced readers"--Subjects--Topical Terms:

185034
Differential equations, Partial
--Numerical solutions.Index Terms--Genre/Form:

214472
Electronic books.

LC Class. No.: QA377 / .F87 2011

Dewey Class. No.: 518/.64

Discrete variational derivative methoda structurepreserving numerical method for partial differential equations /
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020 $z 1420094459 (hardback)
020 $a 9781420094466 (electronic bk.)
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050 0 0 $a QA377 $b .F87 2011
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100 1 $a Furihata, Daisuke. $3 649243
245 1 0 $a Discrete variational derivative method $h [electronic resource] : $b a structurepreserving numerical method for partial differential equations / $c Daisuke Furihata, Takayasu Matsuo.
260 $a Boca Raton, FL : $b Chapman and Hall/CRC, $c c2011.
300 $a 1 online resource (xi, 376 p.) : $b ill.
490 1 $a Chapman & Hall/CRC numerical analysis and scientific computing
504 $a Includes bibliographical references and index.
505 0 $a 1. Introduction and summary of this book An introductory example: the spinodal decomposition - History -- Derivation of dissipative or conservative schemes advanced topics -- 2. Target partial differential equations -- Variational derivatives -- First-order real-valued PDEs -- First-order complex-valued PDEs -- Systems of first-order PDEs -- Second-order PDEs -- 3. Discrete variational derivative method -- Discrete symbols and formulas -- Procedure for first-order real-valued PDEs -- Procedure for first-order complex-valued PDEs -- Procedure for systems of first-order PDEs -- Procedure for second-order PDEs -- Preliminaries on discrete functional analysis -- 4. Applications -- Target PDEs 1 -- Target PDEs 2 -- Target PDEs 3 -- Target PDEs 4 -- Target PDEs 5 -- Target PDEs 7 -- Other equations -- 5. Advanced topic I: design of high-order schemes -- Orders of accuracy of schemes -- Spatially high-order schemes -- Temporally high-order schemes: composition method -- Temporally high-order schemes: high-order discrete variational derivatives -- 6. Advanced topic II: design of linearly-implicit schemes -- Basic idea for constructing linearly-implicit schemes -- Multiple-points discrete variational derivative -- Design of schemes -- Applications -- Remarks on the stability of linearly-implicit schemes -- 7. Advanced topic III: further remarks -- Solving system of nonlinear equations -- Switch to Galerkin framework -- Extension to non-rectangular meshes on 2D Region -- A. Semi-discrete schemes in space B -- Proof of Proposition 3.4.
520 $a "Many important problems in engineering and science are modeled by nonlinear partial differential equations (PDEs). A new trend in PDEs, called structure-preserving numerical methods, has recently developed. This book is devoted to one such technique, called the discrete variational derivative method. First, the text introduces the key factors and the basic ideas of this method, followed by target problems solvable by the method. The second section describes the rigorous mathematics in detail along with relevant applications, which are illustrated by worked examples. It concludes with a comprehensive of listing of essential references on structure-preserving algorithms for advanced readers"-- $c Provided by publisher.
588 $a Description based on print version record.
650 0 $a Differential equations, Partial $x Numerical solutions. $3 185034
650 0 $a Nonlinear theories. $3 182014
650 0 $a Engineering mathematics. $3 182072
655 4 $a Electronic books. $2 local. $3 214472
700 1 $a Matsuo, Takayasu. $3 649244
830 0 $a Chapman & Hall/CRC numerical analysis and scientific computing. $3 574770
856 4 0 $u http://www.crcnetbase.com/isbn/978-1-4200-9445-9