pde2path - a Matlab package for continuation and bifurcation in systems of PDEs

pde2path - a Matlab package for continuation and bifurcation in systems of PDEs, v3.1

Currently maintained by A. Meiners, J. Rademacher, and H. Uecker

Former developers include H. de Witt, T. Dohnal, and D. Wetzel

Home | Tutorials and Demos | Applications| Backlog

New version pde2path 3.1 (September 2023). Download: pde2path (software and demos) tar.gz or zip.
Latest updates:

September 2023: some bugfixes, and new tutorial Continuation of fold points, branch points and Hopf points with constraints
July 2023: version 3.1. First version of library Xcont and demos geomtut for Differential geometric bifurcation problems in pde2path
June 2021: version 3.0, stable version, associated to the book Numerical continuation and bifurcation in Nonlinear PDEs, SIAM.
January 2021: New tutorial pde2path without FEM, explaining mods to run pde2path on "general" right hand sides.
September 2020: most of pde2path now also runs under octave. See README in the folder octave of the pde2path download. Otherwise: bug--fixes, and additional demos (chtor, schnakcone) for problems on curved surfaces, see Pattern formation tutorial [§5 and 6].

For documentation, see the Quickstart guide and reference card and the Tutorials section. For a quick look, here are some movies. For older versions see the Backlog.

pde2path is currently maintained by: Alexander Meiners, Jens Rademacher and Hannes Uecker. Former co--developers: Hannes deWitt, Tomas Dohnal, and Daniel Wetzel.

Many thanks to: Francesca Mazzia for TOM, to Uwe Prüfert for providing OOPDE, to Daniel Kressner for pqzschur, to Kristian Ejlebjaerg Jensen for trullekrul, to Alec Jacobson for the gptoolbox, and to all people from whom we lend (public domain) code, some just small snippets, some large, see also "Licence" below.

For bugs, questions or remarks please write to: hannes.uecker -- at -- uol.de, and/or one of the other current maintainers. Any feedback is welcome.

Abstract. pde2path is a continuation/bifurcation package for systems of PDEs over bounded d-dimensional domains, d=1,2,3, including features such as nonlinear boundary conditions, cylinder and torus geometries (i.e., periodic boundary conditions), and a general interface for adding auxiliary equations like mass conservation or phase equations for continuation of traveling waves. The original version 1.0 was for elliptic systems in 2D and based on the Matlab pdetoolbox, which since v2.3 has been more or less replaced by the free package OOPDE. Recent additions (v2.5 and v2.6) include the handling of multiple steady bifurcation points, Branch point continuation and Hopf point continuation via extended systems, continuation of relative equilibria (e.g., traveling waves and rotating waves), branch switching from periodic orbits (Hopf pitchfork/transcritical bifurcation, and period doubling), and new demos, for instance on pattern formation on spheres and tori (Pattern formation tutorial, § 6), and on the computation of coefficients of amplitude equations for Turing bifurcations (ampsys tutorial, standalone version of ampsys as tar or zip). In v2.7 we added 2D and 3D anisotropic mesh adaptation by trullekrul, and algorithms for canonical paths to canonical periodic states in OC problems, in v2.8 mainly examples of deflation and of periodic orbits in non-autonomous systems, and since v2.9 we aim to maintain octave compatibility. v3.0 is associated with the pde2path book. In v3.1 we added the library Xcont and demos geomtut described in Differential geometric bifurcation problems in pde2path

License
pde2path is free software; you can redistribute it and/or modify it under the terms of the GNU GPL as published by the Free Software Foundation. pde2path is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY. See the GNU GPL for more details. pde2path comes with some third party libraries, partly reduced, and partly modified by the pde2path team. If you want to redistribute (parts of) these libraries yet again, please first get in touch with the respective authors to obtain more information on newer versions and/or full versions. See pde2path/incl3rdpartylibs/README for more information.

Your use of pde2path implies that you agree to this License.

References.
A book describing the use of pde2path, and some of the mathematics behind it, is

H. Uecker, Numerical continuation and bifurcation in Nonlinear PDEs, SIAM, 2021.

A review is given in

H. Uecker, Numerical continuation and bifurcation in Nonlinear PDEs - Algorithms, Applications, and Experiments, Jahresbericht der DMV, 2021.

This also comes with a tutorial and demo files.

The original journal reference for the software (v1.0) and the (original) demos is

H. Uecker, D. Wetzel, J. Rademacher, pde2path - a Matlab package for continuation and bifurcation in 2D elliptic systems, Numerical Mathematics: Theory, Methods and Applications , 7:58-106, 2014.

Here is the old preprint. It also contains some details of the mathematics behind the continuation and bifurcation, some mathematical and modeling background on the example problems, and many references. v2.0 was first described in

T. Dohnal, J. Rademacher, H. Uecker, D. Wetzel, pde2path 2.0: multi-parameter continuation and periodic domains, in Horst Ecker, Alois Steindl, Stefan Jakubek, eds, ENOC 2014 - Proceedings of 8th European Nonlinear Dynamics Conference. preprint.

The Hopf algorithms and basic Hopf demos are described in

H. Uecker, Hopf bifurcation and time periodic orbits with pde2path - algorithms and applications, Communications in Computational Physics, doi: 10.4208/cicp.OA-2017-018, 2018. preprint. Note that the Hopf algorithms have since been significantly extended, see the Hopf tutorial

An overview of applications of pde2path to scalar problems is also given in

S. Engelnkemper, S. V. Gurevich, H. Uecker, D. Wetzel, U. Thiele, Continuation for thin film hydrodynamics and related scalar problems, in Comput. Methods Appl. Sci., 50, Springer, Cham, 2019, preprint