SpectrUW: a laboratory for the numerical exploration of spectra of linear operators. Spectra of linear operators play an important role in various aspects of applied mathematics. For all but the simplest operators, the spectrum cannot be determined analytically and as such it is difficult to build up any intuition about the spectrum. One way to obtain such intuition is to consider many examples numerically and observe emerging patterns. This is feasible using an efficient black-box numerical method, i.e., a method that requires no conceptual changes for different examples. Hill’s method satisfies these requirements. It is the mathematical foundation of SpectrUW (pronounced “spectrum”), mathematical black-box software that serves as a laboratory for the numerical approximation of spectra of one-dimensional linear operators.
Keywords for this software
References in zbMATH (referenced in 10 articles )
Showing results 1 to 10 of 10.
- Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L.Miguel; Zumbrun, Kevin: Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation (2013)
- Sherratt, Jonathan A.: Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations (2013)
- Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L.Miguel; Zumbrun, Kevin: Stability of periodic Kuramoto-Sivashinsky waves (2012)
- Johnson, Mathew A.; Zumbrun, Kevin: Convergence of Hill’s method for nonselfadjoint operators (2012)
- Sherratt, Jonathan A.: Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations (2012)
- Barker, Blake; Johnson, Mathew A.; Rodrigues, L.Miguel; Zumbrun, Kevin: Metastability of solitary roll wave solutions of the St. Venant equations with viscosity (2011)
- Bronski, Jared C.; Johnson, Mathew A.: The modulational instability for a generalized Korteweg-de Vries equation (2010)
- Nivala, Michael; Deconinck, Bernard: Periodic finite-genus solutions of the KdV equation are orbitally stable (2010)
- Hařaǧuş, Mariana; Kapitula, Todd: On the spectra of periodic waves for infinite-dimensional Hamiltonian systems (2008)
- Deconinck, Bernard; Kiyak, Firat; Carter, John D.; Kutz, J.Nathan: SpectrUW: a laboratory for the numerical exploration of spectra of linear operators (2007)