Pde2path - A Matlab Package for Continuation and Bifurcation in 2D Elliptic Systems. Issue 1 (February 2014)

• Record Type: Journal Article
• Authors: Uecker, Hannes; Wetzel, Daniel; Rademacher, Jens D. M.
• Is Part Of: Numerical mathematics. Volume 7:Issue 1(2014)
• Page Start: 58
• Page End: 106
• Publication Date: 2014-02
• Subjects: 35J47, -- 35J60, -- 35B22, -- 65N30; Elliptic systems, -- continuation and bifurcation, -- finite element method; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.1017/S1004897900000295
• Languages: English
• ISSNs: 1004-8979

Abstract

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 fromwww.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.