Magnus integrator and successive approximation for solving time-dependent problems

Juergen Geiser

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 28 pp, 14 figures

MSC 2000

65M15 Error bounds

65L05 Initial value problems

Abstract
Magnus integrator and successive approximation for solving time-dependent problems. The Magnus expansion has been intensely studied and widely applied for solving explicitly time-dependent problems. Due to its exponential character, it is rather difficult to derive practical algorithms beyond the sixth-order. An alternative method is based on successive approximation methods, that taken into account the temporally inhomogeneous equation (method of Tanabe and Sobolevski). In this work, we show that the recently derived ideas of the successive approximation method in a splitting method. Examples are discussed.