Parameter space mapping of first-order linear ordinary differential equations

Lynn M. Hubbard, Carl Wulfman, Herschel Rabitz

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A Lie group formalism for global parameter space mapping of ordinary differential equations, described in the preceding paper, is developed further here. The need for such mapping arises in a variety of physical contexts. The procedure is demonstrated on, but not restricted to, the system of coupled equations Ẋ = cX. The Lie group generators are obtained exactly from both the time-independent and time-dependent generating equations. The transformations obtained from these generators leave the system of differential equations invariant. The time-independent transformations map any solution of the linear system Ẋ = cX into any other solution with the same frequency or time constant. The time-dependent transformations interconvert solutions with different frequencies and/or time constants. Any solution of Ẋ = cX can be mapped into any solution of Ẋ = c′X. Thus the behavior of X (t) can be examined as a function of changes in any of the system parameters, or in the initial conditions, X(0). As an example, one of the time-dependent mappings demonstrates the continuous transformation of oscillator solutions into nonoscillatory ones, and vice versa.

Original languageEnglish (US)
Pages (from-to)2273-2280
Number of pages8
JournalThe Journal of Physical Chemistry
Issue number10
StatePublished - Jan 1 1986

All Science Journal Classification (ASJC) codes

  • General Engineering
  • Physical and Theoretical Chemistry


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