Now showing items 1-4 of 4

    • Efficient rigorous numerics for higher-dimensional PDEs via one-dimensional estimates 

      Gameiro M.; Lessard J.-P. (SIAM Journal on Numerical Analysis, 2013-12-31)
      We present an efficient rigorous computational method which is an extension of the work Analytic Estimates and Rigorous Continuation for Equilibria of Higher-Dimensional PDEs (M. Gameiro and J.-P. Lessard, J. Differential ...
    • Existence of secondary bifurcations or isolas for PDEs 

      Gameiro M.; Lessard J.-P. (Nonlinear Analysis, Theory, Methods and Applications, 2011-12-31)
      In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines ...
    • Rigorous numerics for NLS: Bound states, spectra, and controllability 

      Castelli R.; Teismann H. (Physica D: Nonlinear Phenomena, 2015-12-31)
      In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schrödinger equation (NLS); specifically, to determining bound-state solutions and establishing certain spectral ...
    • Rigorous numerics in floquet theory: Computing stable and unstable bundles of periodic orbits 

      Castelli R.; Lessard J.-P. (SIAM Journal on Applied Dynamical Systems, 2013-12-31)
      In this paper, a rigorous method to compute Floquet normal forms of fundamental matrix solutions of nonautonomous linear differential equations with periodic coefficients is introduced. The Floquet normal form of a fundamental ...