By Daisuke Furihata,Takayasu Matsuo
Nonlinear Partial Differential Equations (PDEs) became more and more vital within the description of actual phenomena. in contrast to usual Differential Equations, PDEs can be utilized to successfully version multidimensional platforms.
The tools recommend in Discrete Variational by-product Method pay attention to a brand new type of "structure-preserving numerical equations" which improves the qualitative behaviour of the PDE ideas and allows sturdy computing. The authors have additionally taken care to offer their tools in an obtainable demeanour, this means that the booklet might be necessary to engineers and physicists with a simple wisdom of numerical research. subject matters mentioned include:
- "Conservative" equations corresponding to the Korteweg–de Vries equation (shallow water waves) and the nonlinear Schrödinger equation (optical waves)
- "Dissipative" equations comparable to the Cahn–Hilliard equation (some part 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 platforms of nonlinear equations utilizing numerical Newton process libraries
Read or Download Discrete Variational Derivative Method: A Structure-Preserving Numerical Method for Partial Differential Equations (Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series) PDF
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