TY - JOUR

T1 - Factorization of certain evolution operators using lie algebra

T2 - Formulation of the method

AU - Demiralp, Metin

AU - Rabitz, Herschel

PY - 1991/12

Y1 - 1991/12

N2 - In this work, a new method to factorize certain evolution operators into an infinite product of simple evolution operators is presented. The method uses Lie operator algebra and the evolution operators are restricted to exponential form. The argument of these forms is a first-order linear partial differential operator. The method has broad applications, including the areas of sensitivity analysis, the solution of ordinary differential equations, and the solution of Liouville's equation. A sequence of ξ-approximants is generated to represent the Lie operators. Under certain conditions, the convergence rate of the ξ-approximant sequences is remarkably high. This work presents the general formulation of the scheme and some simple illustrative examples. Investigation of convergence properties is given in a companion paper.

AB - In this work, a new method to factorize certain evolution operators into an infinite product of simple evolution operators is presented. The method uses Lie operator algebra and the evolution operators are restricted to exponential form. The argument of these forms is a first-order linear partial differential operator. The method has broad applications, including the areas of sensitivity analysis, the solution of ordinary differential equations, and the solution of Liouville's equation. A sequence of ξ-approximants is generated to represent the Lie operators. Under certain conditions, the convergence rate of the ξ-approximant sequences is remarkably high. This work presents the general formulation of the scheme and some simple illustrative examples. Investigation of convergence properties is given in a companion paper.

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U2 - 10.1007/BF01192579

DO - 10.1007/BF01192579

M3 - Article

AN - SCOPUS:34249920474

SN - 0259-9791

VL - 6

SP - 165

EP - 191

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 1

ER -