11 citations · 17 across the 8 of their papers we have counts for
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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…
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…
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…