Magnus and Fer expansions for matrix differential equations: the convergence problem

Authors: Blanes S.¹; Casas F.²; Oteo J.A.¹; Ros J.¹

Source: Journal of Physics A: Mathematical and General, Volume 31, Number 1, 1998 , pp. 259-268(10)

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Abstract:

Approximate solutions of matrix linear differential equations by matrix exponentials are considered. In particular, the convergence issue of Magnus and Fer expansions is treated. Upper bounds for the convergence radius in terms of the norm of the defining matrix of the system are obtained. The very few previously published bounds are improved. Bounds to the error of approximate solutions are also reported. All results are based just on algebraic manipulations of the recursive relation of the expansion generators.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Departament de F?sica Te?rica and IFIC, Universitat de Val?ncia, 46100-Burjassot, Valencia, Spain 2: Departament de Matem?tiques, Universitat Jaume I, 12071-Castell?n, Spain

Publication date: 1998-01-01