Discrete variational derivative method : a structure-preserving numerical method for partial differential equations
著者
書誌事項
Discrete variational derivative method : a structure-preserving numerical method for partial differential equations
（Chapman & Hall/CRC numerical analysis and scientific computing）
CRC Press, c2011
- : hbk
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注記
Includes bibliographical references (p. 359-371) and index
内容説明・目次
内容説明
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 Schroedinger equation (optical waves)
"Dissipative" equations such as the Cahn-Hilliard equation (some phase separation phenomena) and the Newell-Whitehead equation (two-dimensional Benard 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
目次
Introduction and Summary of This Book. Target Partial Differential Equations. Discrete Variational Derivative Method. Applications. Advanced Topic I: Design of High-Order Schemes. Advanced Topic II: Design of Linearly-Implicit Schemes. Advanced Topic III: Further Remarks.
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