Higher order operator splitting methods via Zassenhaus product formula: Theory and applications

Computers and Mathematics with Applications

Volumn 62, Issue 4, 2011, Pages 1994-2015

  Geiser, Jürgen ^a   Tanoǧlu, Gamze ^b   Gücüyenen, Nurcan ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b IZMIR INSTITUTE OF TECHNOLOGY   (Turkey)

Author keywords

Iterative solver method; Operator splitting method; Parabolic differential equations; Weighting methods; Zassenhaus product

Indexed keywords

ITERATIVE SOLVERS; OPERATOR SPLITTING METHOD; PARABOLIC DIFFERENTIAL EQUATION; WEIGHTING METHODS; ZASSENHAUS PRODUCT;

MATHEMATICAL OPERATORS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; SCALES (WEIGHING INSTRUMENTS);

ITERATIVE METHODS;

EID: 80051786451     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.06.043     Document Type: Article

References (18)

1. R.E. Ewing Up-scaling of biological processes and multiphase flow in porous media IIMA Volumes in Mathematics and its Applications vol. 295 2002 Springer-Verlag 195 215
2. J. Geiser, Numerical simulation of a model for transport and reaction of radionuclides, in: Proceedings of the Large Scale Scientific Computations of Engineering and Environmental Problems, Sozopol, Bulgaria, 2001.
3. P. Frolkovi, J. Geiser, Numerical simulation of radionuclides transport in double porosity media with sorption, in: Proceedings of Algorithmy 2000, Conference of Scientific Computing, 2000, pp. 2836.
4. R.I. McLachlan, G. Reinoult, and W. Quispel Splitting methods Acta Numerica 2002 341 434
5. J.A. Oteo The BakerCampbellHausdorff formula and nested commutator identities Journal of Mathematical Physics 32 1991 419
6. I. Farago, J. Geiser, Iterative operator-splitting methods for linear problems, Preprint No. 1043 of the Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany, June 2005.
7. S. Vandewalle, Parallel multigrid waveform relaxation for parabolic problems, Teubner Skripten zur Numerik, B.G. Teubner Stuttgart, 1993.
8. G. Strang On the construction and comparision of difference schemes SIAM Journal on Numerical Analysis 5 1968 506 517
9. G.I Marchuk Some applicatons of splitting-up methods to the solution of problems in mathematical physics Aplikace Matematiky 1 1968 103 132
10. D. Scholz, and M. Weyrauch A note on the Zassenhaus product formula Journal of Mathematical Physics 47 2006 033505
11. S. Descombes Convergence of a splitting method of high order for reactiondiffusion systems Mathematics of Computations 70 2001 1481 1501 (Pubitemid 33582379)
12. J. Geiser, and G. Tanoglu Operator-splitting methods via Zassenhaus product formula Applied Mathematics and Computation 217 2011 4557 4575
13. E. Hairer, C. Lubich, and G. Wanner Geometric numerical integration Springer Series in Computational Mathematics vol. 31 2002 Springer Verlag Berlin, New York, Heidelberg
14. H. Yoshida Construction of higher order symplectic integrators Physics Letters A 150 57 1990
15. J. Geiser Magoules Lai Decomposition Methods for Differential Equations: Theory and Applications 2009 Chapman & Hall/CRC Press, Taylor and Francis Group
16. B. Gustafsson High Order Difference Methods for Time dependent PDE Springer Series in Computational Mathematics vol. 38 2007 Springer Verlag Berlin, New York, Heidelberg
17. X. Lu, Y. Sun, and J.N. Petersen Analytical solutions of TCE transport with convergent reactions Transport in Porous Media 51 2003 211 225 (Pubitemid 36242771)
18. J. Geiser, Gekoppelte Diskretisierungsverfahren f̈r Systeme von Konvektions-Dispersions-Diffusions-Reaktionsgleichungen, Doktor-Arbeit, Universitt Heidelberg, 2003.