pde2path - A Matlab package for continuation and bifurcation in 2D elliptic systems

TL;DR

pde2path is a MATLAB package designed for continuation and bifurcation analysis of 2D elliptic PDE systems, supporting various boundary conditions, stability analysis, and mesh handling, with applications demonstrated through multiple example problems.

Contribution

The paper introduces pde2path, a user-friendly MATLAB package that simplifies bifurcation analysis of 2D elliptic PDEs using FEM, with extensive examples and features.

Findings

Supports arbitrary component systems and boundary conditions.

Includes stability analysis and error control.

Provides templates for common PDE problems.

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-Benard 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.