Volume 7, Issue 1
pde2path - A Matlab Package for Continuation and Bifurcation in 2D Elliptic Systems

Hannes Uecker, Daniel Wetzel & Jens D. M. Rademacher

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 58-106.

Published online: 2014-07

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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 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.

  • Keywords

Elliptic systems, continuation and bifurcation, finite element method.

  • AMS Subject Headings

35J47, 35J60, 35B22, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-7-58, author = {}, title = {pde2path - A Matlab Package for Continuation and Bifurcation in 2D Elliptic Systems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {1}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.1231nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5866.html} }
TY - JOUR T1 - pde2path - A Matlab Package for Continuation and Bifurcation in 2D Elliptic Systems JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 58 EP - 106 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.1231nm UR - https://global-sci.org/intro/article_detail/nmtma/5866.html KW - Elliptic systems, continuation and bifurcation, finite element method. AB -

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.

Hannes Uecker, Daniel Wetzel & Jens D. M. Rademacher. (2020). pde2path - A Matlab Package for Continuation and Bifurcation in 2D Elliptic Systems. Numerical Mathematics: Theory, Methods and Applications. 7 (1). 58-106. doi:10.4208/nmtma.2014.1231nm
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