Generalizations and error analysis of the iterative operator splitting method

Tamás Ladics; István Faragó

Open Mathematics (2013)

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

Abstract

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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.

How to cite

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Tamás 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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  1. [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. [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. [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 Zbl1142.65374
  4. [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. [5] Faragó I., Havasi Á., Operator Splittings and their Applications, Mathematical Research Developments Series, Nova Science, Hauppauge, 2009 
  6. [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. [7] Ladics T., Application of operator splitting to solve reaction-diffusion equations, Electron. J. Qual. Theory Differ. Equ., 2012, 9QTDE Proceedings, #9 
  8. [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. [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. [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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