继续
MATLAB语言
分叉
计算机科学
数学
程序设计语言
物理
非线性系统
量子力学
作者
Hannes Uecker,Daniel Wetzel,Jens D. M. Rademacher
出处
期刊:Numerical Mathematics-theory Methods and Applications
[Global Science Press]
日期:2014-06-01
卷期号:7 (1): 58-106
被引量:91
标识
DOI:10.4208/nmtma.2014.1231nm
摘要
pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with rather general boundary conditions. The package is based on the FEM of the Matlab pdetoolbox, and is explained by a number of examples, including Bratu's problem, the Schnakenberg model, Rayleigh-Benard convection, and von Karman plate equations. These serve as templates to study new problems, for which the user has to provide, via Matlab function files, a description of the geometry, the boundary conditions, the coefficients of the PDE, and a rough initial guess of a solution. The basic algorithm is a one parameter arclength continuation with optional bifurcation detection and branch-switching. Stability calculations, error control and mesh-handling, and some elementary time-integration for the associated parabolic problem are also supported. The continuation, branch-switching, plotting etc are performed via Matlab command-line function calls guided by the AUTO style. The software can be downloaded from this http URL, where also an online documentation of the software is provided such that in this paper we focus more on the mathematics and the example systems.
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