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

Gang Pang (1) , Songsong Ji (2, 3) , Xavier Antoine (4, 5)

1 SMS - School of Mathematical Sciences [Beijing]
2 College of Engineering [Beijing]
3 College of Environmental Sciences and Engineering [Peking]
4 IECL - Institut Élie Cartan de Lorraine
5 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization

The construction of exact absorbing boundary conditions (ABCs) for the one-dimensional nonlocal fully-discrete Schrödinger equation is proposed. The 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. The theory and numerical analysis is supported by numerical examples.

Mots clés: Nonlocal Schrödinger equation; exact absorbing boundary condition; stability and error analysis

Domaines: Equations aux dérivées partielles [math.AP]

Gang Pang, Songsong Ji, Xavier Antoine. Construction and analysis of discretization schemes for one-dimensional nonlocal Schrödinger equations with exact absorbing boundary conditions. 2021. ⟨hal-03281252⟩