11 citations · 17 across the 8 of their papers we have counts for
10 papers
A second-order-in-time scheme for the von Neumann equation with singular self-interaction and simulation of the onset of instability
Agissilaos Athanassoulis, Fotini Karakatsani, Irene Kyza
The von Neumann equation with delta self-interaction kernel serves as a statistical model for nonlinear waves, and it exhibits a bifurcation between stable and unstable regimes. In…
Efficient numerical approximations for a non-conservative Nonlinear Schrodinger equation appearing in wind-forced ocean waves
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza
We consider a non-conservative nonlinear Schrodinger equation (NCNLS) with time-dependent coefficients, inspired by a water waves problem. This problem does not have mass or energy…
Modulation instability and convergence of the random phase approximation for stochastic sea states
Agissilaos G. Athanassoulis, Irene Kyza
The nonlinear Schrödinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial co…
A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza +1
We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrödinger-Poisson system. More specifically, we use the Cr…
Pointwise a posteriori error bounds for blow-up in the semilinear heat equation
Irene Kyza, Stephen Metcalfe
This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for the semilinear heat equation with a general…
-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems
Irene Kyza, Stephen Metcalfe, Thomas Wihler
This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existe…
A posteriori error analysis for evolution nonlinear Schrödinger equations up to the critical exponent
Theodoros Katsaounis, Irene Kyza
We provide a posteriori error estimates in the norm for relaxation time discrete and fully discrete schemes for a class of evolution nonlinear Schrödinger equations…
Adaptivity and blow-up detection for nonlinear evolution problems
Andrea Cangiani, Emmanuil H. Georgoulis, Irene Kyza +1
This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem w…
Regularized semiclassical limits: linear flows with infinite Lyapunov exponents
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza
Semiclassical asymptotics for linear Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of att…
A posteriori error control & adaptivity for Crank-Nicolson finite element approximations for the linear Schrödinger equation
Theodoros Katsaounis, Irene Kyza
We derive optimal order a posteriori error estimates for fully discrete approximations of linear Schrödinger-type equations, in the norm. For the discretization in…