عنوان

Discrete variational derivative method :

(Number (ISBN

1420094459 (hardback)

(Number (ISBN

9781420094459 (hardback)

Number

dltt

Title Proper

Discrete variational derivative method :

General Material Designation

[Book]

Other Title Information

a structure-preserving numerical method for partial differential equations /

First Statement of Responsibility

Daisuke Furihata, Takayasu Matsuo

Place of Publication, Distribution, etc.

Boca Raton, FL :

Name of Publisher, Distributor, etc.

Chapman and Hall/CRC,

Date of Publication, Distribution, etc.

c2011

Specific Material Designation and Extent of Item

xi, 376 p. :

Other Physical Details

ill. ;

Dimensions

25 cm

Series Title

Chapman & Hall/CRC numerical analysis and scientific computing

Text of Note

Includes bibliographical references and index

Text of Note

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

0

Text of Note

"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"--

Differential equations, Partial-- Numerical solutions

Engineering mathematics

Nonlinear theories

Number

Edition

Class number

Book number

Furihata, Daisuke

Matsuo, Takayasu

Date of Transaction

20120604152459.0

Electronic name

[Book]

Y