The Numerov-Crank-Nicolson scheme on a non-uniform mesh for the time-dependent Schrödinger equation on the half-axis

DOI10.3934/krm.2015.8.587zbMath1327.65164OpenAlexW2524439108MaRDI QIDQ888745

Alexander Zlotnik

Publication date: 2 November 2015

Published in: Kinetic and Related Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/krm.2015.8.587

zbMATH Keywords

stabilityerror estimatesfinite difference schemeunbounded domainCrank-Nicolson schemeinitial boundary value problemtime-dependent Schrödinger equationnumerical resultNumerov schemeapproximate transparent boundary conditionsglobal Richardson extrapolation

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)

Related Items (7)

High order compact finite difference schemes on nonuniform grids ⋮ On stability and error bounds of an explicit in time higher-order vector compact scheme for the multidimensional wave and acoustic wave equations ⋮ A random cloud algorithm for the Schrödinger equation ⋮ On construction and properties of compact 4th order finite-difference schemes for the variable coefficient wave equation ⋮ A ``converse stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation ⋮ A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes ⋮ ON COMPACT 4TH ORDER FINITE-DIFFERENCE SCHEMES FOR THE WAVE EQUATION

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