SplittingParameters¶

About the `SplittingParameters` class¶

The WaveBlocks Project

class WaveBlocksND.SplittingParameters[source]¶

build(method)[source]¶

Parameters:	method – A string specifying the method for time integration.
Returns:	Two arrays $a$ and $b$ .

Method	Order	Authors	Reference
LT	1	Lie/Trotter	[1], [3] page 42, equation 5.2
S2	2	Strang	[2], [3] page 42, equation 5.3
SS	2	Strang	[2], [3] page 42, equation 5.3
PRKS6	4	Blanes/Moan	[4] page 318, table 2, ‘S6’
BM42	4	Blanes/Moan	[4] page 318, table 3, ‘SRKNb6’
Y4	4	Yoshida	[5], [3] page 40, equation 4.4
Y61	6	Yoshida	[5], [3] page 144, equation 3.11
BM63	6	Blanes/Moan	[4] page 318, table 3, ‘SRKNa14’
KL6	6	Kahan/Li	[6], [3] page 144, equation 3.12
KL8	8	Kahan/Li	[6], [3] page 145, equation 3.14
KL10	10	Kahan/Li	[6], [3] page 146, equation 3.15

[1]	H.F. Trotter, “On the product of semi-groups of operators”, Proc. Am. Math. Soc.1O (1959) 545-551.

[2]	(1, 2) G. Strang, “On the construction and comparison of difference schemes”, SIAM J. Numer. Anal. 5 (1968) 506-517.

[3]	(1, 2, 3, 4, 5, 6, 7, 8) E. Hairer, C. Lubich, and G. Wanner, “Geometric Numerical Integration - Structure-Preserving Algorithms for Ordinary Differential Equations”, Springer-Verlag, New York, 2002 (Corrected second printing 2004).

[4]	(1, 2, 3) S. Blanes and P.C. Moan, “Practical Symplectic Partitioned Runge-Kutta and Runge-Kutta-Nystrom Methods”, J. Computational and Applied Mathematics, Volume 142, Issue 2, (2002) 313-330.

[5]	(1, 2) H. Yoshida, “Construction of higher order symplectic integrators”, Phys. Lett. A 150 (1990) 262-268.

[6]	(1, 2, 3) W. Kahan and R.-c. Li, “Composition constants for raising the orders of unconventional schemes for ordinary differential equations”, Math. Comput. 66 (1997) 1089-1099.

intsplit(psi1, psi2, a, b, tspan, N, args1=[], args2=[])[source]¶

Compute a single, full propagation step by operator splitting.

Parameters:	psi1 – First evolution operator $\Psi_a$ psi2 – Second evolution operator $\Psi_b$ a – Parameters for evolution with $\Psi_a$ b – Parameters for evolution with $\Psi_b$ tspan – Timespan $t$ of a single, full splitting step N – Number of substeps to perform args1 – Additional optional arguments of $\Psi_a$ args2 – Additional optional arguments of $\Psi_b$

Note

The values for args1 and args2 have to be of type list even in case of single items.

order(method)[source]¶

Parameters:	method – A string specifying the method for time integration.
Returns:	The order of this method.