Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We discuss the structure of the local error of exponential operator splitting methods. In particular, it is shown that the leading error term is a Lie element, i.e., a linear combination of higher-degree commutators of the given operators. This structural assertion can be used to formulate a simple algorithm for the automatic generation of a minimal set of polynomial equations representing the order conditions, for the general case as well as in symmetric settings.
Czasopismo
Rocznik
Tom
Strony
243--256
Opis fizyczny
Bibliogr. 14 poz., tab.
Twórcy
autor
- Institute for Analysis and Scientific Computing Wiedner Hauptstrasse 8–10/E101, A-1040 Vienna, Austria
autor
- Institute for Analysis and Scientific Computing Wiedner Hauptstrasse 8–10/E101, A-1040 Vienna, Austria
Bibliografia
- [1] W. Auzinger, O. Koch, M. Thalhammer, Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part II. Higher order methods for linear problems, J. Comput. Appl. Math. 255 (2013), 384–403.
- [2] W. Auzinger et. al., Adaptive time splitting methods, in preparation.
- [3] S. Blanes, F. Casas, On the convergence and optimization of the Baker-Campbell--Hausdorff formula, Lin. Alg. Appl. 378 (2004), 135–158.
- [4] S. Blanes, P.C. Moan, Practical symplectic partitioned Runge-Kutta and Runge-Kutta--Nyström methods, J. Comput. Appl. Math. 142 (2002), 313–330.
- [5] S. Blanes, F. Casas, P. Chartier, A. Murua, Optimized high-order splitting methods for some classes of parabolic equations, Math. Comp. 82 (2013), 1559–1576.
- [6] S. Blanes, F. Casas, A. Murua, Splitting and composition methods in the numerical integration of differential equations, Bol. Soc. Esp. Mat. Apl. 45 (2008), 89–145.
- [7] P. Chartier, A. Murua, An algebraic theory of order, M2AN Math. Model. Numer. Anal. 43 (2009), 607–630.
- [8] J.-P. Duval, Géneration d’une section des classes de conjugaison et arbre des mots de Lyndon de longueur bornée, Theoret. Comput. Sci. 60 (1988), 255–283.
- [9] E. Hairer, C. Lubich, G. Wanner, Geometrical Numerical Integration – Stucture--Preserving Algorithms for Ordinary Differential Equations, 2nd ed., Springer-Verlag, Berlin, Heidelberg, 2006.
- [10] E. Hansen, A. Ostermann, Exponential splitting for unbounded operators, Math. Comp. 78 (2009), 1485–1496.
- [11] M. Suzuki, General theory of higher-order decomposition of exponential operators and symplectic integrators, Phys. Lett. A 165 (1992), 387–395.
- [12] M. Thalhammer, High-order exponential operator splitting methods for time-dependent Schrödinger equations, SIAM J. Numer. Anal. 46 (2008), 2022–2038.
- [13] Z. Tsuboi, M. Suzuki, Determining equations for higher-order decompositions of exponential operators, Int. J. Mod. Phys. B 09 (1995), 3241–3268.
- [14] H. Yoshida, Construction of higher order symplectic integrators, Phys. Lett. A 150 (1990), 262–268.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bd012efe-78c1-467d-8020-8a7f214b548f