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

Published online by Cambridge University Press:  28 May 2015

Hannes Uecker,
Daniel Wetzel and
Jens D. M. Rademacher
Hannes Uecker*
Affiliation:
Institut für Mathematik, Universität Oldenburg, 26111 Oldenburg, Germany
Daniel Wetzel*
Affiliation:
Institut für Mathematik, Universität Oldenburg, 26111 Oldenburg, Germany
Jens D. M. Rademacher*
Affiliation:
Universität Bremen, Fachbereich Mathematik, Postfach 33 04 40, 28359 Bremen, Germany
*
Corresponding author.Email address:hannes.uecker@uni-oldenburg.de
Corresponding author.Email address:daniel.wetzel@uni-oldenburg.de
Corresponding author.Email address:rademach@math.uni-bremen.de
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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 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 www.staff.uni-oldenburg.de/hannes.uecker/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.

Keywords

35J4735J6035B2265N30Elliptic systemscontinuation and bifurcationfinite element method

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 1 , February 2014, pp. 58 - 106
Copyright
Copyright © Global Science Press Limited 2014

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