Practical splitting methods for the adaptive integration of nonlinear evolution equations. I: Construction of optimized schemes and pairs of schemes

DOI10.1007/s10543-016-0626-9zbMath1359.65080arXiv1604.01179OpenAlexW2336570447WikidataQ55670592 ScholiaQ55670592MaRDI QIDQ512845

Winfried Auzinger, Harald Hofstätter, Othmar Koch, David I. Ketcheson

Publication date: 2 March 2017

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.01179

zbMATH Keywords

free Lie algebranumerical examplesSchrödinger equationevolution equationslocal errorsplitting methodsorder conditionsembedded methods

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions to abstract evolution equations (65J08)

Related Items (11)

Additive splitting methods for parallel solutions of evolution problems ⋮ 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 ⋮ Optimised Trotter decompositions for classical and quantum computing ⋮ High-Order Operator Splitting for the Bidomain and Monodomain Models ⋮ The BCH-Formula and Order Conditions for Splitting Methods ⋮ High-order commutator-free quasi-Magnus exponential integrators for non-autonomous~linear evolution equations ⋮ Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions ⋮ A comparison of fourth-order operator splitting methods for cardiac simulations ⋮ Adaptive time propagation for time-dependent Schrödinger equations ⋮ Splitting Methods for Rotations: Application to Vlasov Equations ⋮ Setup of Order Conditions for Splitting Methods

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