Stability of a Numerov type finite-difference scheme with approximate transparent boundary conditions for the nonstationary Schrödinger equation on the half-axis

DOI10.1007/s10958-010-0040-9zbMath1256.65086OpenAlexW2025064353MaRDI QIDQ548724

A. V. Lapukhina, Alexander Zlotnik

Publication date: 30 June 2011

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-010-0040-9

zbMATH Keywords

stabilityinitial-boundary value problemSchrödinger equationsymmetric 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) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (5)

On a splitting higher-order scheme with discrete transparent boundary conditions for the Schrödinger equation in a semi-infinite parallelepiped ⋮ The Numerov-Crank-Nicolson scheme on a non-uniform mesh for the time-dependent Schrödinger equation on the half-axis ⋮ Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis ⋮ 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

Cites Work

• Family of finite-difference schemes with transparent boundary conditions for the nonstationary Schrödinger equation in a semi-infinite strip
• On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. I
• Discrete transparent boundary conditions for the Schrödinger equation -- a compact higher order scheme
• On a family of finite-difference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation
• On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. II.
• Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability
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