LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
SpectrUW: A laboratory for the numerical exploration of spectra of linear operators
Mathematics and Computers in Simulation
Computing spectra of linear operators using the Floquet-Fourier-Hill method
Journal of Computational Physics
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A variety of numerical methods are available for determining the stability of a given solution of a partial differential equation. However for a family of solutions, calculation of boundaries in parameter space between stable and unstable solutions remains a major challenge. This paper describes an algorithm for the calculation of such stability boundaries, for the case of periodic travelling wave solutions of spatially extended local dynamical systems. The algorithm is based on numerical continuation of the spectrum. It is implemented in a fully automated way by the software package wavetrain, and two examples of its use are presented. One example is the Klausmeier model for banded vegetation in semi-arid environments, for which the change in stability is of Eckhaus (sideband) type; the other is the two-component Oregonator model for the photosensitive Belousov---Zhabotinskii reaction, for which the change in stability is of Hopf type.