Defect-based local error estimators for splitting methods, with application to Schrödinger equations. I: The linear case

DOI10.1016/j.cam.2012.01.001zbMath1238.65091OpenAlexW2114363690MaRDI QIDQ408198

Mechthild Thalhammer, Othmar Koch, Winfried Auzinger

Publication date: 29 March 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2012.01.001

zbMATH Keywords

numerical examplesdefect correctionlinear evolution equationsa posteriori local error estimatesa priori local error estimatesexponential operator splitting methodsLie-Trotter and Strang splitting methodstime-dependent linear Schrödinger equations

Mathematics Subject Classification ID

Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (10)

Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime ⋮ An improved local error estimator for symmetric time-stepping schemes ⋮ Practical splitting methods for the adaptive integration of nonlinear evolution equations. II: Comparisons of local error estimation and step-selection strategies for nonlinear Schrödinger and wave equations ⋮ Optimal parameters for numerical solvers of PDEs ⋮ Symmetrized local error estimators for time-reversible one-step methods in nonlinear evolution equations ⋮ Practical splitting methods for the adaptive integration of nonlinear evolution equations. I: Construction of optimized schemes and pairs of schemes ⋮ Defect-based local error estimators for splitting methods, with application to Schrödinger equations. II: Higher-order methods for linear problems. ⋮ Adaptive time propagation for time-dependent Schrödinger equations ⋮ Defect-based local error estimators for splitting methods, with application to Schrödinger equations. III: The nonlinear case ⋮ Series solutions of non-similarity boundary layer flows of nano-fluids over stretching surfaces

Cites Work

• An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime
• High-order time-splitting Hermite and Fourier spectral methods
• The defect correction principle and discretization methods
• Strang's formula for holomorphic semi-groups
• Error bounds for exponential operator splittings
• On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
• Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods
• Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
• Error control for time-splitting spectral approximations of the semiclassical Schrodinger equation
• High-Order Exponential Operator Splitting Methods for Time-Dependent Schrödinger Equations
• Visual Quantum Mechanics
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