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Discrete Variational Derivative Method, A Structure Preserving Numerical, NEW HC

Undiscovered Galaxy
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Item specifics

Condition
Brand new: A new, unread, unused book in perfect condition with no missing or damaged pages. See the ...
ISBN
9781420094459

About this product

Product Identifiers

Publisher
CRC Press LLC
ISBN-10
1420094459
ISBN-13
9781420094459
eBay Product ID (ePID)
112730868

Product Key Features

Number of Pages
376 Pages
Language
English
Publication Name
Discrete Variational Derivative Method : A Structure-Preserving Numerical Method for Partial Differential Equations
Publication Year
2010
Subject
Differential Equations / General, Number Systems, Differential Equations / Partial, Applied
Type
Textbook
Author
Daisuke Furihata, Takayasu Matsuo
Subject Area
Mathematics
Series
Chapman and Hall/Crc Numerical Analysis and Scientific Computing Ser.
Format
Hardcover

Dimensions

Item Height
1 in
Item Weight
23.2 Oz
Item Length
9.6 in
Item Width
6.4 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
2010-043677
Dewey Edition
22
Reviews
The authors introduce a new class of structure preserving numerical methods which improve the qualitative behavior of solutions of partial differential equations and allow stable computing. ... This book should be useful to engineers and physicists with a basic knowledge of numerical analysis. --Rémi Vaillancourt, Mathematical Reviews, Issue 2011m, The authors introduce a new class of structure preserving numerical methods which improve the qualitative behavior of solutions of partial differential equations and allow stable computing. e This book should be useful to engineers and physicists with a basic knowledge of numerical analysis. e"Rmi Vaillancourt, Mathematical Reviews, Issue 2011m, The authors introduce a new class of structure preserving numerical methods which improve the qualitative behavior of solutions of partial differential equations and allow stable computing. 'e¦ This book should be useful to engineers and physicists with a basic knowledge of numerical analysis. 'e"Rémi Vaillancourt, Mathematical Reviews, Issue 2011m
Illustrated
Yes
Dewey Decimal
515.353
Table Of Content
Preface Introduction and Summary of This Book An Introductory Example: the Spinodal Decomposition History Derivation of Dissipative or Conservative Schemes Advanced Topics Target Partial Differential Equations Variational Derivatives First-Order Real-Valued PDEs First-Order Complex-Valued PDEs Systems of First-Order PDEs Second-Order PDEs 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 Design of Schemes Procedure for Second-Order PDEs Preliminaries on Discrete Functional Analysis Applications Target PDEs Cahn-Hilliard Equation Allen-Cahn Equation Fisher-Kolmogorov Equation Target PDEs Target PDEs Target PDEs Nonlinear Schr¨odinger Equation Target PDEs Zakharov Equations Target PDEs Other Equations Advanced Topic I: Design of High-Order Schemes Orders of Accuracy of the Schemes Spatially High-Order Schemes Temporally High-Order Schemes: With the Composition Method Temporally High-Order Schemes: With High-Order Discrete Variational Derivatives Advanced Topic II: Design of Linearly-Implicit Schemes Basic Idea for Constructing Linearly-Implicit Schemes Multiple-Points Discrete Variational Derivative Design of Schemes Applications Remark on the Stability of Linearly-Implicit Schemes Advanced Topic III: Further Remarks Solving System of Nonlinear Equations Switch to Galerkin Framework Extension to Non-Rectangular Meshes on D Region A Semi-discrete schemes in space B Proof of Proposition 3.4 Bibliography Index
Synopsis
Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of "structure-preserving numerical equations" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineers and physicists with a basic knowledge of numerical analysis. Topics discussed include: "Conservative" equations such as the Korteweg-de Vries equation (shallow water waves) and the nonlinear Schr dinger equation (optical waves) "Dissipative" equations such as the Cahn-Hilliard equation (some phase separation phenomena) and the Newell-Whitehead equation (two-dimensional B nard convection flow) Design of spatially and temporally high-order schemas Design of linearly-implicit schemas Solving systems of nonlinear equations using numerical Newton method libraries, Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of "structure-preserving numerical equations" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineers and physicists with a basic knowledge of numerical analysis. Topics discussed include: "Conservative" equations such as the Korteweg-de Vries equation (shallow water waves) and the nonlinear Schrödinger equation (optical waves) "Dissipative" equations such as the Cahn-Hilliard equation (some phase separation phenomena) and the Newell-Whitehead equation (two-dimensional Bénard convection flow) Design of spatially and temporally high-order schemas Design of linearly-implicit schemas Solving systems of nonlinear equations using numerical Newton method libraries, 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.
LC Classification Number
QA377.F87 2011

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