Related papers: Refined Spectral Method as an extremely accurate t…
Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte…
We study regularity and numerical methods for two-sided fractional diffusion equations with a lower-order term. We show that the regularity of the solution in weighted Sobolev spaces can be greatly improved compared to that in standard…
A spectral method is considered for approximating the fractional Laplacian and solving the fractional Poisson problem in 2D and 3D unit balls. The method is based on the explicit formulation of the eigenfunctions and eigenvalues of the…
We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary…
We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An…
This article is devoted to the construction of new numerical methods for the semiclassical Schr\"odinger equation. A phase-amplitude reformulation of the equation is described where the Planck constant epsilon is not a singular parameter.…
In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schr\"odinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the…
Three pseudospectral algorithms are described (Euler, leapfrog and trapez) for solving numerically the time dependent nonlinear Schroedinger equation in one, two or three dimensions. Numerical stability regions in the parameter space are…
We derive in a straightforward way the exact controllability of the 1-D Schrodinger equation with a Dirichlet boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the…
We present an approach to numerically solving the time-dependent Schroedinger equation and other parabolic equations by the split-step technique with fast Fourier transform, which suppresses the backreflection of waves from the grid…
This paper presents an accurate highly efficient method for solving the bound states in the one-dimensional Schr\"odinger equation with an arbitrary potential. We show that the bound state energies of a general potential well can be…
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
We consider phaseless inverse scattering for the Schr\"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we…
A new type of solution for the full 3+1 dimensional space-time Schroedinger equation is presented here. We consider elegant presentation of the exact solution in a spherical coordinate system, along with the assuming of separation of the…
We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for…
We formulate and implement a spectral method for solving the Schrodinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials…
This paper presents a fast algorithm to solve a spectral estimation problem for two-dimensional random fields. The latter is formulated as a convex optimization problem with the Itakura-Saito pseudodistance as the objective function subject…
The subject of this paper is the design of efficient and stable spectral methods for time-dependent partial differential equations in unit balls. We commence by sketching the desired features of a spectral method, which is defined by a…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
This paper is concerned with the design of two different classes of Galerkin boundary element methods for the solution of high-frequency sound-hard scattering problems in the exterior of two-dimensional smooth convex scatterers. Both…