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pde2path - A Matlab Package for Continuation and Bifurcation in 2D Elliptic Systems

pde2path - A Matlab Package for Continuation and Bifurcation in 2D Elliptic Systems
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Year:    2014

Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 1 : pp. 58–106

Abstract

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-Bénard 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 timeintegration 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 www.staff.uni-oldenburg.de/hannes.ue ker/pde2path, 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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2014.1231nm

Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 1 : pp. 58–106

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    49

Keywords:    Elliptic systems continuation and bifurcation finite element method.

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