81
Views
2
CrossRef citations to date
0
Altmetric
Section B

Stabilization theory of iterative operator-splitting methods

Pages 1857-1871 | Received 17 Jun 2008, Accepted 01 Oct 2008, Published online: 26 Jun 2009

References

  • Barbu , V. 1998 . Partial Differential Equations and Boundary Value Problems , Dordrecht, Boston, London : Mathematics and its Applications, Kluwer Academic Publishers .
  • Deuflhard , P. 2004 . Newton Methods for Nonlinear Problems , Springer Series in Computational Mathematics Vol. 35 , Heidelberg, New York : Springer .
  • Emmrich , E. 2004 . Gewöhnliche und Operator-Differentialgleichungen , Wiesbaden : Vieweg Verlag .
  • Engel , K.-J. and Nagel , R. 2000 . One-Parameter Semigroups for Linear Evolution Equations , Heidelberg, New York : Springer-Verlag .
  • Farago , I. 2005 . Splitting Methods for Abstract Cauchy Problems , Vol. 3401 , 35 – 45 . Berlin : Springer-Verlag . Lecture Notes in Computer Science
  • Farago , I. 2008 . Modified Iterated Operator-Splitting Method . Applied Mathematical Modelling , 32 ( 8 ) : 1542 – 1551 .
  • Farago , I. and Geiser , J. 2007 . Iterative operator-splitting methods for linear problems . Int. J. Comput. Sci. Eng. , 3 ( 4 ) : 255 – 263 .
  • Geiser , J. 2008 . Iterative operator-splitting methods with higher-order time-integration methods and applications for parabolic partial differential equations . J. Comput. Appl. Math. , 217 : 227 – 242 .
  • Geiser , J. 2009 . Consistency of iterative operator-splitting methods: theory and applications . Numer. Methods Partial Differ. Equ. , DOI: 10.1002/num.20422
  • Geiser , J. and Kravvaritis , C. 2008 . Overlapping operator-splitting methods and applications in stiff differential equations . Neural Parallel Sci. Comput. , 16 : 189 – 200 .
  • Hairer , E. , Lubich , C. and Wanner , G. 2002 . Geometric numerical integration: structure-preserving algorithms for ordinary differential equations , Springer Series in Computational Mathematics Vol. 31 , Heidelberg, New York : Springer-Verlag Berlin .
  • Hu , S. and Papageorgiou , N. S. 2000 . Handbook of Multivalue Analysis I,II , Dordrecht : Kluwer . Part I: 1997, Part II
  • Hundsdorfer , W. H. and Verwer , J. 2003 . Numerical Solution of Time-dependent Advection–Diffusion–Reaction equations , Berlin : Springer-Verlag .
  • Kanney , J. , Miller , C. and Kelley , C. 2003 . Convergence of iterative split-operator approaches for approximating nonlinear reactive transport problems . Adv. Water Res. , 26 : 247 – 261 .
  • Karlson , K. H. and Lie , K. A. 1999 . An unconditionally stable splitting scheme for a class of nonlinear parabolic equations . IMA J. Numer. Anal. , 19 ( 4 ) : 604 – 635 .
  • Kelley , C. T. 2003 . “ Solving Nonlinear Equations with Newton's Method ” . In Computational Mathematics , Vol. XIV , Philadelphia, , USA : SIAM .
  • Marchuk , G. I. 1968 . Some applications of splitting-up methods to the solution of problems in mathematical physics . Apl. Mat. , 1 : 103 – 132 .
  • Ruzicka , M. 2004 . Nichtlineare Funktionalanalysis , Heidelberg, New York : Springer-Verlag, Berlin .
  • Strang , G. 1968 . On the construction and comparison of difference schemes . SIAM J. Numer. Anal. , 5 : 506 – 517 .
  • Verwer , J. G. and Sportisse , B. 1998 . A note on operator-splitting in a stiff linear case . MAS-R9830 , ISSN 1386-3703
  • Zeidler , E. 1990 . “ Nonlinear Monotone Operators ” . In Nonlinear Functional Analysis and its Applications , Vol. II/B , Heidelberg, New York : Springer-Verlag, Berlin .
  • Zlatev , Z. 1995 . Computer Treatment of Large Air Pollution Models , Dordrecht, , The Netherlands : Kluwer Academic Publishers .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.