Generalizations and error analysis of the iterative operator splitting method

• Autorzy: Tamás Ladics , István Faragó
• Języki publikacji: EN

Abstrakty

EN

The properties of iterative splitting with two bounded linear operators have been analyzed by Faragó et al. For more than two operators, iterative splitting can be defined in many different ways. A large class of the possible extensions to this case is presented in this paper and the order of accuracy of these methods are examined. A separate section is devoted to the discussion of two of these methods to illustrate how this class of possible methods can be classified with respect to the order of accuracy.

Słowa kluczowe

EN

Bounded linear operators; Iterative operator splitting; Order of accuracy; Diffusion-reaction equation

Kategorie tematyczne

• 65M06: Finite difference methods
• 65L05: Initial value problems
• 35K57: Reaction-diffusion equations
• 34A30: Linear equations and systems, general

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 8
• Strony: 1416-1428

Daty

wydano

2013-08-01

online

2013-05-22

Twórcy

autor

Tamás Ladics

• Szent István University

autor

István Faragó

Bibliografia

• [1] Bjørhus M., Operator splitting for abstract Cauchy problems, IMA J. Numer. Anal., 1998, 18(3), 419–443 http://dx.doi.org/10.1093/imanum/18.3.419
• [2] Faragó I., Geiser J., Iterative operator-splitting methods for linear problems, International Journal of Computational Science and Engineering, 2007, 3(4), 255–263
• [3] Faragó I., Gnandt B., Havasi Á., Additive and iterative operator splitting methods and their numerical investigation, Comput. Math. Appl., 2008, 55(10), 2266–2279 http://dx.doi.org/10.1016/j.camwa.2007.11.017
• [4] Faragó I., Havasi Á., The mathematical background of operator splitting and the effect of non-commutativity, In: Lecture Notes in Comput. Sci., 2179, Springer, Berlin-Heidelberg, 2001, 264–271
• [5] Faragó I., Havasi Á., Operator Splittings and their Applications, Mathematical Research Developments Series, Nova Science, Hauppauge, 2009
• [6] Ladics T., Analysis of the splitting error for advection-reaction problems in air pollution models, Quarterly Journal of the Hungarian Meteorological Service, 2005, 109(3), 173–188
• [7] Ladics T., Application of operator splitting to solve reaction-diffusion equations, Electron. J. Qual. Theory Differ. Equ., 2012, 9QTDE Proceedings, #9
• [8] Kanney J.F., Miller C.T., Kelley C.T., Convergence of iterative split-operator approaches for approximating nonlinear reactive transport problems, Adv. in Water Res., 2003, 26(3), 247–261 http://dx.doi.org/10.1016/S0309-1708(02)00162-8
• [9] Sanz-Serna J.M., Geometric integration, In: The State of the Art in Numerical Analysis, York, April, 1996, Inst. Math. Appl. Conf. Ser. New Ser., 63, Clarendon/Oxford University Press, New York, 1997, 121–143
• [10] Zlatev Z., Dimov I., Computational and Numerical Challenges in Environmental Modelling, Stud. Comput. Math., 13, Elsevier, Amsterdam, 2006

Identyfikatory

DOI

10.2478/s11533-013-0246-4