2022
DOI: 10.1016/j.amc.2021.126700
|View full text |Cite
|
Sign up to set email alerts
|

High order integrators obtained by linear combinations of symmetric-conjugate compositions

Abstract: A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions obtained from a basic time-symmetric integrator of order 2n (n ≥ 1). The new integrators are of order 2(n + k), k = 1, 2, . . ., and preserve time-symmetry up to order 4n + 3 when applied to differential equations with real vector fields. If in addition the system is Hamiltonian and the basic sch… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1

Citation Types

0
4
0

Year Published

2022
2022
2023
2023

Publication Types

Select...
1
1

Relationship

0
2

Authors

Journals

citations
Cited by 2 publications
(4 citation statements)
references
References 21 publications
0
4
0
Order By: Relevance
“…Just this year Casas, Escorihuela-Tomàs and different collaborators have published several works on higher order symplectic integrators with complex coefficients [12,[33][34][35]. Again, as Omelyan et al [1] did with real coefficients, they do not optimise for general Trotter decompositions.…”
Section: Using Complex Coefficientsmentioning
confidence: 99%
See 1 more Smart Citation
“…Just this year Casas, Escorihuela-Tomàs and different collaborators have published several works on higher order symplectic integrators with complex coefficients [12,[33][34][35]. Again, as Omelyan et al [1] did with real coefficients, they do not optimise for general Trotter decompositions.…”
Section: Using Complex Coefficientsmentioning
confidence: 99%
“…From section 3.2 we expect the following order for the order n = 4 schemes from least to most efficient, that is from largest to smallest asymptotic error: Forest-Ruth (31), Suzuki (38), Omelyan's Forest-Ruth-type (33), uniform non-unitary (44), Blanes and Moan (46), our optimised 4th order (40), non-unitary (q = 4) (36), and non-unitary (q = 5) (42). Furthermore we expect large gaps between Forest-Ruth, the other unitary schemes, and the non-unitary schemes.…”
Section: Real Time Evolution Of the Heisenberg Modelmentioning
confidence: 99%
“…Just this year Casas, Escorihuela-Tomàs and different collaborators have published several works on higher order symplectic integrators with complex coefficients [12,[31][32][33]. Again, as Omelyan [1] did with real coefficients, they do not optimise for general Trotter decompositions.…”
Section: Using Complex Coefficientsmentioning
confidence: 99%
“…Eff 4 = 4.24 (31) has the highest possible efficiency for the given choice of order n = 4 and q = 4 cycles using real coefficients. When Omelyan et al search for the optimal scheme with q = 5 cycles, they apply too many constraints and fail to identify the decomposition scheme (37) derived here for the first time.…”
Section: 24mentioning
confidence: 99%