Discrete Variational Derivative Method

A Structure-Preserving Numerical Method for Partial Differential Equations

By: Daisuke Furihata, Takayasu Matsuo

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Hardcover | 9 December 2010 | Edition Number 1

At a Glance

Hardcover
390 Pages

Dimensions(cm)
23.4 x 15.6 x 2.24

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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 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

Industry 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.
-Remi Vaillancourt, Mathematical Reviews, Issue 2011m

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