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2012 | 10 | 1 | 159-172
Tytuł artykułu

Richardson Extrapolation combined with the sequential splitting procedure and the θ-method

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
1
Strony
159-172
Opis fizyczny
Daty
wydano
2012-02-01
online
2011-12-09
Twórcy
Bibliografia
  • [1] Anderson E., Bai Z., Bischof C., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., Ostrouchov S., Sorensen D., LAPACK: Users’ Guide, SIAM, Philadelphia, 1992
  • [2] Burrage K., Parallel and Sequential Methods for Ordinary Differential Equations, Numer. Math. Sci. Comput., Oxford University Press, New York, 1992
  • [3] Butcher J.C., Numerical Methods for Ordinary Differential Equations, 2nd ed., John Wiley & Sons, Chichester, 2008 http://dx.doi.org/10.1002/9780470753767
  • [4] Chin S.A., Geiser J., Multi-product operator splitting as a general method of solving autonomous and nonautonomous equations, IMA J. Numer. Anal. (in press), DOI: 10.1093/imanum/drq022
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  • [7] Faragó I., Havasi Á., Operator Splittings and their Applications, Math. Res. Dev. Ser., Nova Science Publishers, Hauppauge, 2009
  • [8] Faragó I., Havasi Á., Zlatev Z., Efficient implementation of stable Richardson extrapolation algorithms, Comput. Math. Appl., 2010, 60(8), 2309–2325 http://dx.doi.org/10.1016/j.camwa.2010.08.025
  • [9] Faragó I., Thomsen P.G., Zlatev Z., On the additive splitting procedures and their computer realization, Appl. Math. Model., 2008, 32(8), 1552–1569 http://dx.doi.org/10.1016/j.apm.2007.04.017
  • [10] Geiser J., Tanoglu G., Operator-splitting methods via the Zassenhaus product formula, Appl. Math. Comput., 2011, 217(9), 4557–4575 http://dx.doi.org/10.1016/j.amc.2010.11.007
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  • [14] Richardson L.F., The deferred approach to the limit I. Single lattice, Philos. Trans. Roy. Soc. London Ser. A, 1927, 226, 299–349 http://dx.doi.org/10.1098/rsta.1927.0008
  • [15] Simpson D., Fagerli H., Jonson J.E., Tsyro S., Wind P., Tuovinen J.-P., Transboundary Acidification, Eutrophication and Ground Level Ozone in Europe. I, Unified EMEP Model Description, EMEP/MSC-W Status Report, 1/2003, Norwegian Meteorological Institute, Oslo, 2003
  • [16] Wilkinson J.H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford-London, 1965
  • [17] Zlatev Z., Modified diagonally implicit Runge-Kutta methods, SIAM J. Sci. Statist. Comput., 1981, 2(3), 321–334 http://dx.doi.org/10.1137/0902026
  • [18] Zlatev Z., Computer Treatment of Large Air Pollution Models, Environmental Science and Technology Library, 2, Kluwer, Dordrecht-Boston-London, 1995 http://dx.doi.org/10.1007/978-94-011-0311-4
  • [19] Zlatev Z., Dimov I., Computational and Numerical Challenges in Environmental Modelling, Stud. Comput. Math., 13, Elsevier, Amsterdam, 2006
  • [20] Zlatev Z., Faragó I., Havasi Á., Stability of the Richardson extrapolation applied together with the θ-method, J. Comput. Appl. Math., 2010, 235(2), 507–517 http://dx.doi.org/10.1016/j.cam.2010.05.052
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0099-7
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