The norm convergence of a Magnus expansion method

András Bátkai; Eszter Sikolya

Open Mathematics (2012)

  • Volume: 10, Issue: 1, page 150-158
  • ISSN: 2391-5455

Abstract

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We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method is investigated.

How to cite

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András Bátkai, and Eszter Sikolya. "The norm convergence of a Magnus expansion method." Open Mathematics 10.1 (2012): 150-158. <http://eudml.org/doc/269757>.

@article{AndrásBátkai2012,
abstract = {We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method is investigated.},
author = {András Bátkai, Eszter Sikolya},
journal = {Open Mathematics},
keywords = {Magnus method; Evolution family; C0-semigroups; evolution family},
language = {eng},
number = {1},
pages = {150-158},
title = {The norm convergence of a Magnus expansion method},
url = {http://eudml.org/doc/269757},
volume = {10},
year = {2012},
}

TY - JOUR
AU - András Bátkai
AU - Eszter Sikolya
TI - The norm convergence of a Magnus expansion method
JO - Open Mathematics
PY - 2012
VL - 10
IS - 1
SP - 150
EP - 158
AB - We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method is investigated.
LA - eng
KW - Magnus method; Evolution family; C0-semigroups; evolution family
UR - http://eudml.org/doc/269757
ER -

References

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  1. [1] Bátkai A., Csomós P., Farkas B., Nickel G., Operator splitting for non-autonomous evolution equations, J. Funct. Anal., 2011, 260(7), 2163–2190 http://dx.doi.org/10.1016/j.jfa.2010.10.008 Zbl1232.65103
  2. [2] Engel K.-J., Nagel R., One-Parameter Semigroups for Linear Evolution Equations, Grad. Texts in Math., 194, Springer, New York, 2000 Zbl0952.47036
  3. [3] Faragó I., Horváth R., Havasi Á., Numerical solution of the Maxwell equations in time-varying medium using Magnus expansion, Cent. Eur. J. Math., 2012, 10(1), 137–149 http://dx.doi.org/10.2478/s11533-011-0074-3 Zbl1243.78049
  4. [4] Hochbruck M., Lubich Ch., On Magnus integrators for time-dependent Schrödinger equations, SIAM J. Numer. Anal., 2003, 41(3), 945–963 http://dx.doi.org/10.1137/S0036142902403875 Zbl1049.65064
  5. [5] Hochbruck M., Ostermann A., Exponential integrators, Acta Numer., 2010, 19, 209–286 http://dx.doi.org/10.1017/S0962492910000048 Zbl1242.65109
  6. [6] Iserles A., Marthinsen A., Nørsett S.P., On the implementation of the method of Magnus series for linear differential equations, BIT, 1999, 39(2), 281–304 http://dx.doi.org/10.1023/A:1022393913721 Zbl0933.65077
  7. [7] Iserles A., Munthe-Kaas H.Z., Nørsett S.P., Zanna A., Lie-group methods, Acta Numer., 2000, 9, 215–365 http://dx.doi.org/10.1017/S0962492900002154 Zbl1064.65147
  8. [8] Magnus W., On the exponential solution of differential equations for a linear operator, Comm. Pure Appl. Math., 1954, 7(4), 649–673 http://dx.doi.org/10.1002/cpa.3160070404 Zbl0056.34102
  9. [9] Nickel G., Evolution semigroups and product formulas for nonautonomous Cauchy problems, Math. Nachr., 2000, 212, 101–116 http://dx.doi.org/10.1002/(SICI)1522-2616(200004)212:1<101::AID-MANA101>3.0.CO;2-3 

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