Fast computation of limit cycles in an industrial application

Shay Gueron and Nadav Liron
Additional contact information
Shay Gueron: University of Haifa, Department of Mathematics
Nadav Liron: Technion — I.I.T, Department of Mathematics

A chapter in Practical Asymptotics, 2001, pp 79-86 from Springer

Abstract: Abstract A model problem is described that requires the study of a system of the form $$ \dot v $$ = ɛF P (v(t), t) which depends on a set of parameters P, and where ɛ ≪ 1. The problem comes from an industrial application where it is a kernel of an optimization procedure. The optimization depends on computing the limit cycle, and the problem needs to be solved repeatedly. Short computation time is therefore essential. The naive approach is to integrate the equation forward in time, starting from an arbitrary initial condition, until the transients disappear and the limit cycle is approximated within a given tolerance. This approach is too slow and thus impractical in the context of the optimization procedure. The problem involves two types of asymptotic considerations: long-time asymptotic s and small-parameter asymptotics. Here a simple approach is demonstrated, based on implementing the averaging method. This reduces the solution time to the point that the optimization procedure becomes feasible.

Keywords: limit cycle; dynamical systems; Poincaré-Bendixson (search for similar items in EconPapers)
Date: 2001
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-0698-9_6

Ordering information: This item can be ordered from
http://www.springer.com/9789401006989

DOI: 10.1007/978-94-010-0698-9_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().