Discrete Variational Derivative Method: A Structure-Preserving Numerical Method for Partial Differential...

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Daisuke Furihata (Osaka University, Toyonaka, Japan) Takayasu Matsuo (University of Tokyo, Bunkyo, Japan)

Discrete Variational Derivative Method

A Structure-Preserving Numerical Method for Partial Differential Equations

Daisuke Furihata (Osaka University, Toyonaka, Japan), Takayasu Matsuo (University of Tokyo, Bunkyo, Japan), Frederic Magoules , Choi-Hong Lai

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English

Chapman & Hall/CRC
09 December 2010

Differential calculus & equations; Maths for computer scientists

Series: Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

"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 Schrodinger 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"

By: Daisuke Furihata (Osaka University Toyonaka Japan), Takayasu Matsuo (University of Tokyo, Bunkyo, Japan)
Series edited by: Frederic Magoules, Choi-Hong Lai
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Volume: v. 13
Dimensions: Height: 234mm, Width: 156mm, Spine: 25mm
Weight: 657g
ISBN: 9781420094459
ISBN 10: 1420094459
Series: Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series
Pages: 376
Publication Date: 09 December 2010
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Daisuke Furihata, Takayasu Matsuo

Reviews for Discrete Variational Derivative Method: A Structure-Preserving Numerical Method for Partial Differential Equations

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. -Remi Vaillancourt, Mathematical Reviews, Issue 2011m