Discrete Variational Derivative Method: A Structure-Preserving Numerical Method for Partial Differential Equations - Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series (Hardback)Daisuke Furihata (author), Takayasu Matsuo (author)
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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 Schroedinger 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 schemasDesign of linearly-implicit schemasSolving systems of nonlinear equations using numerical Newton method libraries
Publisher: Taylor & Francis Ltd
Number of pages: 376
Weight: 658 g
Dimensions: 235 x 156 x 25 mm
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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