Construction and analysis of discretization schemes for one-dimensional nonlocal Schrödinger equations with exact absorbing boundary conditions

Gang Pang; Songsong Ji; Xavier Antoine

doi:10.1016/j.cam.2023.115623

Construction and analysis of discretization schemes for one-dimensional nonlocal Schrödinger equations with exact absorbing boundary conditions

Gang Pang^*
, Songsong Ji
, Xavier Antoine

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The construction of exact absorbing boundary conditions (ABCs) for the one-dimensional nonlocal fully-discrete Schrödinger equation is proposed. An efficient computation of the Green's functions for the discrete nonlocal Schrödinger equation is stated and used to build the ABCs. Numerical error estimates are then proved for the case of a singular interaction kernel through a novel way. The theory and numerical analysis is supported by numerical examples.

Original language	English
Article number	115623
Journal	Journal of Computational and Applied Mathematics
Volume	440
DOIs	https://doi.org/10.1016/j.cam.2023.115623
State	Published - Apr 2024

Keywords

Exact absorbing boundary condition
Nonlocal Schrödinger equation
Stability and error analysis

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10.1016/j.cam.2023.115623

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title = "Construction and analysis of discretization schemes for one-dimensional nonlocal Schr{\"o}dinger equations with exact absorbing boundary conditions",

abstract = "The construction of exact absorbing boundary conditions (ABCs) for the one-dimensional nonlocal fully-discrete Schr{\"o}dinger equation is proposed. An efficient computation of the Green's functions for the discrete nonlocal Schr{\"o}dinger equation is stated and used to build the ABCs. Numerical error estimates are then proved for the case of a singular interaction kernel through a novel way. The theory and numerical analysis is supported by numerical examples.",

keywords = "Exact absorbing boundary condition, Nonlocal Schr{\"o}dinger equation, Stability and error analysis",

author = "Gang Pang and Songsong Ji and Xavier Antoine",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2024",

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doi = "10.1016/j.cam.2023.115623",

language = "英语",

volume = "440",

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AU - Pang, Gang

AU - Ji, Songsong

AU - Antoine, Xavier

PY - 2024/4

Y1 - 2024/4

N2 - The construction of exact absorbing boundary conditions (ABCs) for the one-dimensional nonlocal fully-discrete Schrödinger equation is proposed. An efficient computation of the Green's functions for the discrete nonlocal Schrödinger equation is stated and used to build the ABCs. Numerical error estimates are then proved for the case of a singular interaction kernel through a novel way. The theory and numerical analysis is supported by numerical examples.

AB - The construction of exact absorbing boundary conditions (ABCs) for the one-dimensional nonlocal fully-discrete Schrödinger equation is proposed. An efficient computation of the Green's functions for the discrete nonlocal Schrödinger equation is stated and used to build the ABCs. Numerical error estimates are then proved for the case of a singular interaction kernel through a novel way. The theory and numerical analysis is supported by numerical examples.

KW - Exact absorbing boundary condition

KW - Nonlocal Schrödinger equation

KW - Stability and error analysis

UR - https://www.scopus.com/pages/publications/85175717119

U2 - 10.1016/j.cam.2023.115623

DO - 10.1016/j.cam.2023.115623

M3 - 文章

AN - SCOPUS:85175717119

SN - 0377-0427

VL - 440

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 115623

ER -

Construction and analysis of discretization schemes for one-dimensional nonlocal Schrödinger equations with exact absorbing boundary conditions

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Keywords

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