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

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by Daisuke Furihata & Takayasu Matsuo
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Discrete Variational Derivative Method: A Structure-Preserving Numerical Method for Partial Differential Equations by Daisuke Furihata & Takayasu Matsuo

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 librari

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Ebook Details
Pages: 376
Size: 15.3 MB
Publisher: CRC Press
Date published:   2010
ISBN: 9781420094466 (DRM-PDF)

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This product is listed in the following categories:

Nonfiction > Mathematics > Applied
Nonfiction > Mathematics > Differential Equations
Nonfiction > Mathematics > Number Systems

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