A fast BDF2 Galerkin finite element method for the one-dimensional time-dependent Schrödinger equation with artificial boundary conditions

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Partial differential equations of mathematical physics and other areas of application (35Qxx)

Cites Work

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Local artificial boundary conditions for Schrödinger and heat equations by using high-order azimuth derivatives on circular artificial boundary
Convergence of difference scheme for heat equation in unbounded domains using artificial boundary conditions
A finite-difference method for the one-dimensional time-dependent Schrödinger equation on unbounded domain
Exact artifical boundary conditions for the Schrödinger equation in \(\mathbb R ^2\)
Analysis of finite element method for one-dimensional time-dependent Schrödinger equation on unbounded domain
Convergence of a finite element scheme for the two-dimensional time-dependent Schrödinger equation in a long strip
Numerical solution of problems on unbounded domains. A review
Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation.
Fast evaluation of nonreflecting boundary conditions for the Schrödinger equation in one dimension
Fast and stable evaluation of the exact absorbing boundary condition for the semi-discrete linear Schrödinger equation in unbounded domains
High-order local non-reflecting boundary conditions: a review
Exact boundary condition for semi-discretized Schrödinger equation and heat equation in a rectangular domain
The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions
Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability
Optimal finite difference grids and rational approximations of the square root I. Elliptic problems
Near-Optimal Perfectly Matched Layers for Indefinite Helmholtz Problems
Complete Radiation Boundary Conditions: Minimizing the Long Time Error Growth of Local Methods
Fast Evaluation of Artificial Boundary Conditions for Advection Diffusion Equations
On the efficient computation of high-dimensional integrals and the approximation by exponential sums
Fast Numerical Solution of Nonlinear Volterra Convolution Equations
Radiation boundary conditions for acoustic and elastic wave calculations
On Optimal Finite-Difference Approximation of PML
Error Estimates for the Finite Element Approximation of Problems in Unbounded Domains
Stability and Error Analysis for a Second-Order Fast Approximation of the One-dimensional Schrödinger Equation Under Absorbing Boundary Conditions
Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation
An Efficient Second-Order Finite Difference Method for the One-Dimensional Schrödinger Equation with Absorbing Boundary Conditions
Fast Convolution for Nonreflecting Boundary Conditions
Artificial Boundary Method
Boundary Integral Equation Methods for the Two-Dimensional Fluid-Solid Interaction Problem
Boundary Element Methods
Implementation of transparent boundaries for numerical solution of the Schröder equation.
Fast artificial boundary method for the heat equation on unbounded domains with strip tails

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