Convergence of the Magnus Series (English)

In: Foundations of Computational Mathematics   ;  8 ,  3  ;  291-301  ;  2007

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Abstract The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals the fundamental solution of the differential equation. The question considered in this paper is: When does the series converge? The main result establishes a sufficient condition for convergence, which improves on several earlier results.

Table of contents – Volume 8, Issue 3

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287
Foreword
| 2008
291
Convergence of the Magnus Series
Moan, Per Christian / Niesen, Jitse | 2007
303
Symmetric Exponential Integrators with an Application to the Cubic Schrödinger Equation
Celledoni, Elena / Cohen, David / Owren, Brynjulf | 2007
319
Spectral Semi-discretisations of Weakly Non-linear Wave Equations over Long Times
Hairer, E. / Lubich, C. | 2007
335
Explicit Volume-Preserving Splitting Methods for Linear and Quadratic Divergence-Free Vector Fields
McLachlan, R. I. / Munthe-Kaas, H. Z. / Quispel, G. R. W. / Zanna, A. | 2007
357
On the Linear Stability of Splitting Methods
Blanes, Sergio / Casas, Fernando / Murua, Ander | 2007
395
On Spherical Averages of Radial Basis Functions
Baxter, B. J. C. | 2008