The norm convergence of a Magnus expansion method

• Autorzy: András Bátkai , Eszter Sikolya
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Magnus method; Evolution family; C0-semigroups

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 65J10: Equations with linear operators (do not use )
• 34K06: Linear functional-differential equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 1
• Strony: 150-158

Daty

wydano

2012-02-01

online

2011-12-09

Twórcy

autor

András Bátkai

• Eötvös Loránd University

autor

Eszter Sikolya

• Eötvös Loránd University

Bibliografia

• [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
• [2] Engel K.-J., Nagel R., One-Parameter Semigroups for Linear Evolution Equations, Grad. Texts in Math., 194, Springer, New York, 2000
• [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
• [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
• [5] Hochbruck M., Ostermann A., Exponential integrators, Acta Numer., 2010, 19, 209–286 http://dx.doi.org/10.1017/S0962492910000048
• [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
• [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
• [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
• [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

Identyfikatory

DOI

10.2478/s11533-011-0101-4