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 …

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 …

A popular approach for proving a posteriori error bounds in various norms for evolution
problems with partial differential equations uses reconstruction operators to recover …

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 …

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 …

We consider a non-conservative nonlinear Schrodinger equation (NCNLS) with time-
dependent coefficients, inspired by a water waves problem. This problem does not have …

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 …

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 …

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 …

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 …