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On the solution of linear differential equations in Lie groups

By England Cb Ew, A. Iserles, A. Iserles, S.P. Nørsett, S. P. Nrsett, Y( Y and Where Y G


The subject matter of this paper is the solution of the linear differential equation y 0 = a(t)y, y(0) = y0 , where y0 2 G, a( \Delta ) : R + ! g and g is a Lie algebra of the Lie group G. By building upon an earlier work of Wilhelm Magnus [16], we represent the solution as an infinite series whose terms are indexed by binary trees. This relationship between the infinite series and binary trees leads both to a convergence proof and to a constructive computational algorithm. This numerical method requires the evaluation of a large number of multivariate integrals but this can be accomplished in a tractable manner by using quadrature schemes in a novel manner and by exploiting the structure of the Lie algebra

Year: 1997
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