Defect-based local error estimators for high-order splitting methods involving three linear operators

DOI10.1007/s11075-014-9935-8zbMath1325.65131OpenAlexW2095610153MaRDI QIDQ745225

Othmar Koch, Mechthild Thalhammer, Winfried Auzinger

Publication date: 13 October 2015

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://phaidra.univie.ac.at/o:423891

zbMATH Keywords

numerical exampleSchrödinger equationinitial boundary value problemslocal errorlinear evolution equationsa posteriori local error estimatorshigh-order exponential operator splitting methodstime integration methodsvariation-of-constant formula

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) NLS equations (nonlinear Schrödinger equations) (35Q55) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical solutions to abstract evolution equations (65J08)

Related Items (7)

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 ⋮ 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 ⋮ Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions ⋮ Adaptive time propagation for time-dependent Schrödinger equations ⋮ GPU acceleration of splitting schemes applied to differential matrix equations ⋮ Setup of Order Conditions for Splitting Methods

Cites Work

• Unnamed Item
• A splitting of the Frobenius morphism on the whole algebra of distributions of \(\mathrm{SL}_2\)
• A class of Uzawa-SOR methods for saddle point problems
• Splitting methods with complex times for parabolic equations
• Localization of triangulated categories and derived categories
• Embedded exponential operator splitting methods for the time integration of nonlinear evolution equations
• Dynamics of rotating two-component Bose-Einstein condensates and its efficient computation
• Two-grid finite volume element method for linear and nonlinear elliptic problems
• An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates
• Structured preconditioners for nonsingular matrices of block two-by-two structures
• Robin functions and extremal functions
• Ground States and Dynamics of Multicomponent Bose--Einstein Condensates
• Bounds on Eigenvalues of Matrices Arising from Interior-Point Methods
• Local error structures and order conditions in terms of Lie elements for exponential splitting schemes
• ON THE GROSS–PITAEVSKII EQUATION WITH STRONGLY ANISOTROPIC CONFINEMENT: FORMAL ASYMPTOTICS AND NUMERICAL EXPERIMENTS

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