Coefficients of various splitting methods

References

The following list contains some selected references from the literature to the described methods and their construction.

1. W. Auzinger, H. Hofstätter, D. Ketcheson, O. Koch, Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes, BIT Numer. Math. 57(1) (2017), 55-74.


2. W. Auzinger, W. Herfort, Local error structures and order conditions in terms of Lie elements for exponential splitting schemes, Opuscula Mathematica 34 (2014), 243-255.


3. W. Auzinger, O. Koch, M. Thalhammer, Defect-based local error estimators for high-order splitting methods involving three linear operators, Numer. Algorithms 70 (2015), 61-91.


4. S. Blanes, S., Casas, F., P. Chartier, A. Murua, Optimized high-order splitting methods for some classes of parabolic equations, Math. Comp. 82 (2013), pp.1559-1576.


5. S. Blanes, S., P.C. Moan, Practical Symplectic Partitioned Runge-Kutta and Runge-Kutta-Nyström Methods, J. Comput. Appl. Math. 142 (2002), pp. 313-330.


6. F. Castella, P. Chartier, S. Descombes, G. Vilmart, Splitting methods with complex times for parabolic equations, BIT Numer. Math. 49 (2009), pp. 487-508.


7. J. Chambers, Symplectic integrators with complex time steps, AJ 126 (2003), pp. 1119-1126.


8. W. Kahan, S., R.-C. Li, Composition constants for raising the order of unconventional schemes for ordinary differential equations, Math. Comp. 66 (1997), pp. 1089-1099.


9. H. Yoshida, Construction of higher order symplectic intergrators, Phys. Lett. A 150 (1990), pp. 262-268.