Discrete Variational Derivative Method - A Structure-Preserving Numerical Method for Partial Differential Equations (Hardcover)

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 Schr dinger equation (optical waves) * "Dissipative" equations such as the Cahn-Hilliard equation (some phase separation phenomena) and the Newell-Whitehead equation (two-dimensional B nard 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

General

Imprint:	Chapman & Hall/CRC
Country of origin:	United States
Series:	Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series
Release date:	December 2010
First published:	2011
Authors:	Daisuke Furihata • Takayasu Matsuo
Dimensions:	234 x 156 x 26mm (L x W x T)
Format:	Hardcover
Pages:	376
ISBN-13:	978-1-4200-9445-9
Categories:	Books > Computing & IT > General theory of computing > Mathematical theory of computation Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers
LSN:	1-4200-9445-9
Barcode:	9781420094459

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