Non-existence of generalized splitting methods with positive coefficients of order higher than four

DOI10.1016/j.aml.2019.05.017OpenAlexW2951476975WikidataQ127873757 ScholiaQ127873757MaRDI QIDQ2274899

Othmar Koch, Winfried Auzinger, Harald Hofstätter

Publication date: 1 October 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.05492

zbMATH Keywords

numerical time integrationpositive coefficientsgeneralized splitting methodsnon-reversible evolution equations

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for ordinary differential equations (65L99) Method of lines for boundary value problems involving PDEs (65N40) 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 ⋮ Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrödinger Equation ⋮ Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type ⋮ Symmetric-conjugate splitting methods for evolution equations of parabolic type ⋮ 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

Cites Work

• Non-satisfiability of a positivity condition for commutator-free exponential integrators of order higher than four
• On the necessity of negative coefficients for operator splitting schemes of order higher than two
• Symplectic integrators from composite operator factorizations
• Solving Linear Partial Differential Equations by Exponential Splitting
• Computations in a free Lie algebra
• Nth-Order Operator Splitting Schemes and Nonreversible Systems
• Local error structures and order conditions in terms of Lie elements for exponential splitting schemes
• Geometric Numerical Integration

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