In this work, the issue of favorable numerical methods for the space and time discretization
of low-dimensional nonlinear Schrödinger equations is addressed. The objective is to …

Recent tensor network techniques for simulating system-environment wave functions have
provided profound insights into non-Markovian dissipation and decoherence in open …

We present and analyze two numerical methods for the logarithmic Schrödinger equation
(LogSE) consisting of a regularized splitting method and a regularized conservative Crank …

The main goal of this chapter is to give the reader a (relatively) brief overview of operator-
splitting, augmented Lagrangian and ADMM methods and algorithms. Following a general …

This article deals with the numerical integration in time of nonlinear Schrödinger
equations. The main application is the numerical simulation of rotating Bose--Einstein …

In this paper the error estimates are derived for Lie-Trotter operator splitting spectral method
for semiclassical linear fractional Schrödinger equation. We first establish a priori estimates …

The logarithmic nonlinearity has been used in many partial differential equations (PDEs) for
modeling problems in various applications. Due to the singularity of the logarithmic function …

As a basic principle, benefits of adaptive discretisations are an improved balance between
required accuracy and efficiency as well as an enhancement of the reliability of numerical …

In this paper we mathematically characterize through a Lie formalism the local errors
induced by operator splitting when solving nonlinear reaction-diffusion equations, especially …

We prove an error estimate for a Lie--Trotter splitting operator associated with the
Schrödinger--Poisson equation in the semiclassical regime, when the WKB approximation …