Discrete Variational Derivative Method
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A Semi-discrete schemes in space
A01=Daisuke Furihata
A01=Takayasu Matsuo
advanced PDE solution strategies
Author_Daisuke Furihata
Author_Takayasu Matsuo
BBM
boundary
Boundary Term
C3 System
Category=PBKJ
Category=UYAM
Composition Method
computational physics
condition
conservation
Conservation Properties
Conservative Schemes
decomposition
Discrete Boundary Condition
Discrete Energy
Discrete L2 Norm
Discrete Variational Derivative Method
dissipation
Dissipation Property
Dissipative Scheme
energy
Energy Function
eq_bestseller
eq_computing
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
equation
Explicit Euler Scheme
High Order Schemes
high-order numerical schemes
Implicit Euler Scheme
Inexact Newton Methods
kV K44
landau
Linear PDE
Lyapunov Functional
Nonlinear PDE
Nonlinear Schemes
nonlinear wave equations
numerical analysis methods
Periodic Boundary Condition
phase separation modeling
property
Regularized Long Wave Equation
spatial discretization techniques
spinodal
Target Partial Differential Equations
Target PDEs
Type D1
Variational Derivative
Variational Derivatives
Product details
- ISBN 9781420094459
- Weight: 657g
- Dimensions: 156 x 234mm
- Publication Date: 09 Dec 2010
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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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
Daisuke Furihata, Takayasu Matsuo
