The Lie-Trotter splitting for nonlinear evolutionary problems with critical parameters: a compact local error representation and application to nonlinear Schrodinger equations in the semiclassical regime

DOI10.1093/imanum/drs021zbMath1266.65153OpenAlexW2317460055MaRDI QIDQ4920243

Stéphane Descombes, Mechthild Thalhammer

Publication date: 16 May 2013

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imanum/drs021

zbMATH Keywords

stability convergence numerical examples semiclassical regime error bounds spectral method local error Gross-Pitaevskii equation exponential operator splitting methods Lie-Trotter splitting nonlinear evolutionary problems time-dependent nonlinear Schrödinger equations

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (15)

Lie-Trotter operator splitting spectral method for linear semiclassical fractional Schrödinger equation ⋮ Observable Error Bounds of the Time-Splitting Scheme for Quantum-Classical Molecular Dynamics ⋮ Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime ⋮ Error estimates of local energy regularization for the logarithmic Schrödinger equation ⋮ Optimal parameters for numerical solvers of PDEs ⋮ Symmetrized local error estimators for time-reversible one-step methods in nonlinear evolution equations ⋮ Splitting methods for the nonlocal Fowler equation ⋮ Efficient exponential splitting spectral methods for linear Schrödinger equation in the semiclassical regime ⋮ Multiscale splitting method for the Boltzmann-Poisson equation: application to the dynamics of electrons ⋮ On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit. II. Analytic regularity ⋮ Strang splitting for a semilinear Schrödinger equation with damping and forcing ⋮ Defect-based local error estimators for splitting methods, with application to Schrödinger equations. III: The nonlinear case ⋮ Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation ⋮ Regularized numerical methods for the logarithmic Schrödinger equation ⋮ High Order Exponential Integrators for Nonlinear Schrödinger Equations with Application to Rotating Bose--Einstein Condensates

This page was built for publication: The Lie-Trotter splitting for nonlinear evolutionary problems with critical parameters: a compact local error representation and application to nonlinear Schrodinger equations in the semiclassical regime