PMID- 17166011
OWN - NLM
STAT- MEDLINE
DCOM- 20070215
LR  - 20061214
IS  - 0021-9606 (Print)
IS  - 0021-9606 (Linking)
VI  - 125
IP  - 21
DP  - 2006 Dec 7
TI  - The functional equation truncation method for approximating slow invariant 
      manifolds: a rapid method for computing intrinsic low-dimensional manifolds.
PG  - 214103
AB  - A slow manifold is a low-dimensional invariant manifold to which trajectories 
      nearby are rapidly attracted on the way to the equilibrium point. The exact 
      computation of the slow manifold simplifies the model without sacrificing 
      accuracy on the slow time scales of the system. The Maas-Pope intrinsic 
      low-dimensional manifold (ILDM) [Combust. Flame 88, 239 (1992)] is frequently 
      used as an approximation to the slow manifold. This approximation is based on a 
      linearized analysis of the differential equations and thus neglects curvature. We 
      present here an efficient way to calculate an approximation equivalent to the 
      ILDM. Our method, called functional equation truncation (FET), first develops a 
      hierarchy of functional equations involving higher derivatives which can then be 
      truncated at second-derivative terms to explicitly neglect the curvature. We 
      prove that the ILDM and FET-approximated (FETA) manifolds are identical for the 
      one-dimensional slow manifold of any planar system. In higher-dimensional spaces, 
      the ILDM and FETA manifolds agree to numerical accuracy almost everywhere. 
      Solution of the FET equations is, however, expected to generally be faster than 
      the ILDM method.
FAU - Roussel, Marc R
AU  - Roussel MR
AD  - Department of Chemistry and Biochemistry, University of Lethbridge, Lethbridge, 
      Alberta T1K 3M4, Canada. roussel@uleth.ca
FAU - Tang, Terry
AU  - Tang T
LA  - eng
PT  - Journal Article
PT  - Research Support, Non-U.S. Gov't
PL  - United States
TA  - J Chem Phys
JT  - The Journal of chemical physics
JID - 0375360
SB  - IM
MH  - *Algorithms
MH  - Binding Sites
MH  - Kinetics
MH  - Models, Theoretical
MH  - *Nonlinear Dynamics
MH  - Numerical Analysis, Computer-Assisted
EDAT- 2006/12/15 09:00
MHDA- 2007/02/16 09:00
CRDT- 2006/12/15 09:00
PHST- 2006/12/15 09:00 [pubmed]
PHST- 2007/02/16 09:00 [medline]
PHST- 2006/12/15 09:00 [entrez]
AID - 10.1063/1.2402172 [doi]
PST - ppublish
SO  - J Chem Phys. 2006 Dec 7;125(21):214103. doi: 10.1063/1.2402172.