The splitting in potential Crank–Nicolson scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip

DOI10.1051/M2AN/2014004zbMath1315.65072arXiv1303.3471OpenAlexW2963057642MaRDI QIDQ2936547

Ilya Zlotnik, Alexander Zlotnik, Bernard Ducomet

Publication date: 17 December 2014

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.3471

zbMATH Keywords

algorithm stability fast Fourier transform error analysis initial boundary value problem time-dependent Schrödinger equation numerical result strang splitting tunnel effect approximate and discrete transparent boundary conditions Crank-Nicolson finite-difference scheme

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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On a splitting higher-order scheme with discrete transparent boundary conditions for the Schrödinger equation in a semi-infinite parallelepiped ⋮ Cross‐impact of beam local wavenumbers on the efficiency of self‐adaptive artificial boundary conditions for two‐dimensional nonlinear Schrödinger equation ⋮ Fast Fourier solvers for the tensor product high-order FEM for a Poisson type equation ⋮ On a Numerov-Crank-Nicolson-Strang scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip ⋮ Splitting in Potential Finite-Difference Schemes with Discrete Transparent Boundary Conditions for the Time-Dependent Schrödinger Equation

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