A posteriori error estimation for Magnus-type integrators
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 1, pp. 197-218.

We study high-order Magnus-type exponential integrators for large systems of ordinary differential equations defined by a time-dependent skew-Hermitian matrix. We construct and analyze defect-based local error estimators as the basis for adaptive stepsize selection. The resulting procedures provide a posteriori information on the local error and hence enable the accurate, efficient, and reliable time integration of the model equations. The theoretical results are illustrated on two numerical examples .

DOI : 10.1051/m2an/2018050
Classification : 65L05, 65L20, 65L50, 65L70
Mots-clés : Non-autonomous linear differential equations, magnus-type integrators, a posteriori local error estimation, asymptotical correctness, adaptive stepsize selection
Auzinger, Winfried 1 ; Hofstätter, Harald 1 ; Koch, Othmar 1 ; Quell, Michael 1 ; Thalhammer, Mechthild 1

1 
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     author = {Auzinger, Winfried and Hofst\"atter, Harald and Koch, Othmar and Quell, Michael and Thalhammer, Mechthild},
     title = {A posteriori error estimation for {Magnus-type} integrators},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {197--218},
     publisher = {EDP-Sciences},
     volume = {53},
     number = {1},
     year = {2019},
     doi = {10.1051/m2an/2018050},
     mrnumber = {3937352},
     zbl = {1416.65188},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2018050/}
}
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Auzinger, Winfried; Hofstätter, Harald; Koch, Othmar; Quell, Michael; Thalhammer, Mechthild. A posteriori error estimation for Magnus-type integrators. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 1, pp. 197-218. doi : 10.1051/m2an/2018050. http://www.numdam.org/articles/10.1051/m2an/2018050/

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