Generalizations and error analysis of the iterative operator splitting method

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• 作者：Tamás Ladics (1246)
  István Faragó (2246) (3246)
  
• 关键词：34A30 ; 35K57 ; 65L05 ; 65M06 ; Bounded linear operators ; Iterative operator splitting ; Order of accuracy ; Diffusion ; reaction equation
• 刊名：Central European Journal of Mathematics
• 出版年：2013
• 出版时间：August 2013
• 年：2013
• 卷：11
• 期：8
• 页码：1416-1428
• 全文大小：1102KB
• 参考文献：1. Bj?rhus M., Operator splitting for abstract Cauchy problems, IMA J. Numer. Anal., 1998, 18(3), 419-43 CrossRef
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  3. Faragó I., Gnandt B., Havasi á., Additive and iterative operator splitting methods and their numerical investigation, Comput. Math. Appl., 2008, 55(10), 2266-279 CrossRef
  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, 264-71
  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), 173-88
  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), 247-61 CrossRef
  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, 121-43
  10. Zlatev Z., Dimov I., Computational and Numerical Challenges in Environmental Modelling, Stud. Comput. Math., 13, Elsevier, Amsterdam, 2006
  
• 作者单位：Tamás Ladics (1246)
  István Faragó (2246) (3246)
  
  1246. Department of Mathematics, Ybl Miklós College of Building, Szent István University, Th?k?ly way 74, 1146, Budapest, Hungary
  2246. Institute of Mathematics, E?tv?s Loránd University, Pázmány P. stny. 1/C, 1117, Budapest, Hungary
  3246. HAS-ELTE Research Group “Numerical Analysis and Large Networks- Pázmány P. stny. 1/C, 1117, Budapest, Hungary
  
• ISSN：1644-3616

文摘

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.