The semiclassically scaled time-dependent multi-particle Schrödinger equation describes,
inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational …

In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation
(NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well …

We construct quantum algorithms to compute the solution and/or physical observables of
nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations …

We present the asymptotic transitions from microscopic to macroscopic physics, their
computational challenges and the asymptotic-preserving (AP) strategies to compute …

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive
Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By …

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 computation of the semiclassical Schrödinger equation presents major challenges
because of the presence of a small parameter. Assuming periodic boundary conditions, the …