Rademacher, Jens D. M.; Sandstede, Björn; Scheel, Arnd Computing absolute and essential spectra using continuation. (English) Zbl 1119.65114 Physica D 229, No. 2, 166-183 (2007). A continuation approach to the computation of essential and absolute spectra of differential operators on the real line is presented. The advantages of this approach are the efficient and accurate computation of selected parts of the spectrum (typically those near the imaginary axis) and the option to compute nonlinear travelling waves and selected eigenvalues or other stability indicators simultaneously in order to locate accurately the onset to instability. The implementation and usage with the software package AUTO is discussed and example computations for the Fitzhugh-Nagumo and the complex Ginzburg-Landau equations are presented. Reviewer: Wilhelm Heinrichs (Essen) Cited in 57 Documents MSC: 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 47F05 General theory of partial differential operators 35P15 Estimates of eigenvalues in context of PDEs 35Q35 PDEs in connection with fluid mechanics Keywords:spectral stability; continuation; absolute spectrum; instability thresholds; reaction-diffusion systems; numerical examples; nonlinear travelling waves; eigenvalues; Ginzburg-Landau equations; Fitzhugh-Nagumo equation Software:Eigtool; Trilinos; AUTO2000; AUTO; HomCont PDFBibTeX XMLCite \textit{J. D. M. Rademacher} et al., Physica D 229, No. 2, 166--183 (2007; Zbl 1119.65114) Full Text: DOI Link References: [1] Briggs, R. J., Electron-Stream Interaction with Plasmas (1964), MIT Press: MIT Press Cambridge [2] E. Crampin, Reaction-diffusion patterns on growing domains. 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