We examine various integration schemes for the time-dependent Kohn–Sham equations.
Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear …

Real-time time-dependent density functional theory (RT-TDDFT) is an attractive tool to
model quantum dynamics by real-time propagation without the linear response …

In this paper, we propose a μ-mode integrator for computing the solution of stiff evolution
equations. The integrator is based on a d-dimensional splitting approach and uses exact …

The ability to engineer high-fidelity gates on quantum processors in the presence of
systematic errors remains the primary barrier to achieving quantum advantage. Quantum …

Quantum optimal control theory is becoming increasingly crucial as quantum devices
become more precise, but the need to quickly optimize these systems classically remains a …

We propose a novel algorithm for the temporal integration of the resistive
magnetohydrodynamics (MHD) equations. The approach is based on exponential …

This manuscript summarizes the outcome of the focus groups at" The f (A) bulous workshop
on matrix functions and exponential integrators", held at the Max Planck Institute for …

Rational exponential integrators (REXI) are a class of numerical methods that are well suited
for the time integration of linear partial differential equations with imaginary eigenvalues …

Inversion of ground‐penetrating radar signals requires accurate and efficient forward
modelling. The symplectic Euler method promises good results when simulating ground …

We consider the numerical integration of the Schrödinger equation with a time-dependent
Hamiltonian given as the sum of the kinetic energy and a time-dependent potential …