Click Here to Download: https://ouo.io/VQplYu Discrete Variational Derivative Method A Structure-Preserving Numerical Method for Partial Differential Equations By: Daisuke Furihata Publisher: Chapman and Hall/CRC Print ISBN: 9781420094459, 1420094459 eText ISBN: 9781420094466, 1420094467 Edition: 1st Copyright year: 2010 Format: PDF Available from $ 23.18 USD SKU 9781420094466R90 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 Kortewegâde Vries equation (shallow water waves) and the nonlinear Schrödinger equation (optical waves) Dissipative equations such as the CahnâHilliard 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 libraries
