Discrete Variational Derivative Method A Structure-Preserving Numerical Method for Partial Differential Equations Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series
Auteurs : Furihata Daisuke, Matsuo Takayasu
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
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.
Date de parution : 12-2010
Ouvrage de 350 p.
15.6x23.4 cm
Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).
Prix indicatif 142,05 €
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Mots-clés :
Variational Derivative; Discrete Boundary Condition; Target Partial Differential Equations; Dissipation Property; Discrete Variational Derivative Method; Periodic Boundary Condition; Variational Derivatives; Conservation Properties; Target PDEs; Dissipative Scheme; A Semi-discrete schemes in space; Discrete Energy; Energy Function; Conservative Schemes; Regularized Long Wave Equation; High Order Schemes; Boundary Term; Composition Method; Nonlinear Schemes; Explicit Euler Scheme; C3 System; kV K44; Type D1; Implicit Euler Scheme; BBM; Lyapunov Functional; Linear PDE; Nonlinear PDE; Discrete L2 Norm; Inexact Newton Methods