Factorization of certain evolution operators using lie algebra: Formulation of the method

Metin Demiralp, Herschel Albert Rabitz

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)165-191
Number of pages27
JournalJournal of Mathematical Chemistry
Volume6
Issue number1
DOIs
StatePublished - Dec 1 1991

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Applied Mathematics

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