# Generalizations and error analysis of the iterative operator splitting method

Open Mathematics (2013)

- Volume: 11, Issue: 8, page 1416-1428
- ISSN: 2391-5455

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topTamás Ladics, and István Faragó. "Generalizations and error analysis of the iterative operator splitting method." Open Mathematics 11.8 (2013): 1416-1428. <http://eudml.org/doc/268971>.

@article{TamásLadics2013,

abstract = {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.},

author = {Tamás Ladics, István Faragó},

journal = {Open Mathematics},

keywords = {Bounded linear operators; Iterative operator splitting; Order of accuracy; Diffusion-reaction equation; bounded linear operators; iterative operator splitting; order of accuracy; diffusion-reaction equation},

language = {eng},

number = {8},

pages = {1416-1428},

title = {Generalizations and error analysis of the iterative operator splitting method},

url = {http://eudml.org/doc/268971},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Tamás Ladics

AU - István Faragó

TI - Generalizations and error analysis of the iterative operator splitting method

JO - Open Mathematics

PY - 2013

VL - 11

IS - 8

SP - 1416

EP - 1428

AB - 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.

LA - eng

KW - Bounded linear operators; Iterative operator splitting; Order of accuracy; Diffusion-reaction equation; bounded linear operators; iterative operator splitting; order of accuracy; diffusion-reaction equation

UR - http://eudml.org/doc/268971

ER -

## References

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- [2] Faragó I., Geiser J., Iterative operator-splitting methods for linear problems, International Journal of Computational Science and Engineering, 2007, 3(4), 255–263
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- [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 Zbl1031.65094
- [5] Faragó I., Havasi Á., Operator Splittings and their Applications, Mathematical Research Developments Series, Nova Science, Hauppauge, 2009
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- [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 Zbl0886.65074
- [10] Zlatev Z., Dimov I., Computational and Numerical Challenges in Environmental Modelling, Stud. Comput. Math., 13, Elsevier, Amsterdam, 2006 Zbl1120.65103

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