Practical symplectic partitioned Runge--Kutta and Runge--Kutta--Nyström methods

By Sergio Blanes, Per Christian Moan. 2002

250 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6bad6aa32c6d70a0c264318651e8f4da3fee733c

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In Computational Theory and Mathematics

In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

Geometric integrators for ODEs (2006, methodology): “) A good fourth-order method of this class, due to Blanes and Moan [14], is given by equation (5) together with m = 6 and a0 = a6 = 0.”
Fourth-and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems (2006, methodology): “The following fourth-order methods are compared: (i) the symplectic integrators given by the standard 3-stage method for a general splitting (S4) and the 6-stage scheme for Nyström problems (SRKN4) and the splitting (45) [9,20,13]; (ii) the standard 4-stage Runge–Kutta method (RK4) (it uses the Loba”
Splitting methods (2002, unknown): “Blanes and Moan (2000) have made a detailed study of the order conditions for this case, and find 4th-order methods with error constants 1.32, 0.64, 0.36, and 0.29 for methods with 3, 4, 5, and 6 stages respectively, and 6th-order methods with error constants 1.02, 0.78, and 0.63 with 7, 11, and 14…”
Lax‐Wendroff and Nyström methods for seismic modelling (2009, methodology): “Some optimized symplectic Nyström algorithms have also been developed (Blanes and Moan 2002; Lunk and Simen 2005).”
Scrambling and thermalization in a diffusive quantum many-body system (2016, methodology): “For each of the steps we combine a fourth-order partitioned Runge–Kuttamethod [51]with even–odd bond splitting of theHamiltonian.”
The Magnus expansion and some of its applications (2008, methodology): “(303) In Table 1 we collect the coefficients aij , bij to be used in (302) to obtain the coefficients ρij , σij to be used in the scheme (303) for two methods, denoted by GS6-4 in the general case (whose coefficients ai1, bi1 correspond to S6 in [27]) and MN6-4 when [B(ti), [B(tj), [B(tk), A(tl)]]] ”