A posteriori error analysis for approximations of time-fractional subdiffusion problems
L Banjai, C Makridakis - Mathematics of Computation, 2022 - ams.org
In this paper we consider a sub-diffusion problem where the fractional time derivative is
approximated either by the L1 scheme or by Convolution Quadrature. We propose new …
approximated either by the L1 scheme or by Convolution Quadrature. We propose new …
Error estimation of the relaxation finite difference scheme for the nonlinear Schrödinger equation
GE Zouraris - SIAM Journal on Numerical Analysis, 2023 - SIAM
We consider an initial-and boundary-value problem for the nonlinear Schrödinger equation
with homogeneous Dirichlet boundary conditions in the one space dimension case. We …
with homogeneous Dirichlet boundary conditions in the one space dimension case. We …
Lower bounds, elliptic reconstruction and a posteriori error control of parabolic problems
EH Georgoulis, CG Makridakis - IMA Journal of Numerical …, 2023 - academic.oup.com
A popular approach for proving a posteriori error bounds in various norms for evolution
problems with partial differential equations uses reconstruction operators to recover …
problems with partial differential equations uses reconstruction operators to recover …
Error estimation of the Besse relaxation scheme for a semilinear heat equation
GE Zouraris - ESAIM: Mathematical Modelling and Numerical …, 2021 - esaim-m2an.org
The solution to the initial and Dirichlet boundary value problem for a semilinear, one
dimensional heat equation is approximated by a numerical method that combines the Besse …
dimensional heat equation is approximated by a numerical method that combines the Besse …
On the convergence of a linearly implicit finite element method for the nonlinear Schrödinger equation
M Asadzadeh, GE Zouraris - Studies in Applied Mathematics, 2024 - Wiley Online Library
We consider a model initial‐and Dirichlet boundary–value problem for a nonlinear
Schrödinger equation in two and three space dimensions. The solution to the problem is …
Schrödinger equation in two and three space dimensions. The solution to the problem is …
Efficient numerical approximations for a non-conservative Nonlinear Schrodinger equation appearing in wind-forced ocean waves
We consider a non-conservative nonlinear Schrodinger equation (NCNLS) with time-
dependent coefficients, inspired by a water waves problem. This problem does not have …
dependent coefficients, inspired by a water waves problem. This problem does not have …
On the reflection of solitons of the cubic nonlinear Schrödinger equation
T Katsaounis, D Mitsotakis - Mathematical Methods in the …, 2018 - Wiley Online Library
In this paper, we perform a numerical study on the interesting phenomenon of soliton
reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the …
reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the …
[HTML][HTML] A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems
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 …
approximating solutions of the Schrödinger-Poisson system. More specifically, we use the …
[PDF][PDF] A NOVEL RELAXATION SCHEME FOR THE NUMERICAL APPROXIMATION OF SCHRÖDINGER-POISSON TYPE SYSTEMS
A ATHANASSOULIS, T KATSAOUNIS, I KYZA… - 2022 - researchgate.net
We introduce a new second order in time relaxation-type scheme for approximating
solutions of the Schrödinger-Poisson system. More specifically, we use the Crank-Nicolson …
solutions of the Schrödinger-Poisson system. More specifically, we use the Crank-Nicolson …
[PDF][PDF] A new Besse-type relaxation scheme for the numerical approximation of the Schrödinger-Poisson system.
We introduce a new second order in time Besse-type relaxation scheme for approximating
solutions of the Schrödinger-Poisson system. More specifically, we use the Crank-Nicolson …
solutions of the Schrödinger-Poisson system. More specifically, we use the Crank-Nicolson …