We consider time-dependent (linear and nonlinear) Schrödinger equations in a
semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive …

We compare the long-time error bounds and spatial resolution of finite difference methods
with different spatial discretizations for the Dirac equation with small electromagnetic …

We propose the frozen Gaussian approximation for computation of high frequency wave
propagation. This method approximates the solution to the wave equation by an integral …

The Gaussian beam superposition method is an asymptotic method for computing high
frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the …

The Dirac equation is an important model in relativistic quantum mechanics. In the semi-
classical regime $\epsilon\ll1 $, even a spatially spectrally accurate time splitting method\cite …

We present efficient and accurate numerical methods for computing the ground state and
dynamics of the nonlinear Schrödinger equation (NLSE) with nonlocal interactions based on …

For the Dirac equation with potentials characterized by a small parameter ε∈(0, 1], the
numerical methods for long-time dynamics have received more and more attention …

The frozen Gaussian approximation, proposed in [J. Lu and X. Yang, Commun. Math. Sci., 9
(2011), pp. 663–683], is an efficient computational tool for high frequency wave propagation …

In this paper we propose a class of high order numerical methods to delta function integrals
appearing in level set methods in the three dimensional case by extending the idea for …

This manuscript studies the exact solitary wave profiles for the conformable Schrödinger–
Poisson dynamical system. This system has a significant role in gravity's quantum state …