zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On optimal shooting intervals. (English) Zbl 0532.65054

In this interesting and well written paper, the authors consider in detail the issue of the optimal positioning of shooting points in a multiple shooting algorithm, for first order linear boundary value problems. A good mix of theoretical insight and reasonable heuristic is used to derive strategies for optimizing the shooting points position, with respect to computing time and stability. The resulting criterium is that of ”equidistributing the shooting points.” By this, it is meant that the shooting points should be chosen so that in each subinterval the number of mesh points used by the integrator is constant.

A number of suggestions are made to improve the efficiency of (any) multiple shooting code. Among the most important we mention: a) Use the adaptive mesh integrator only once, when computing the particular solution, and then use the same mesh for computing the fundamental solution: b) Do condensation of several shooting intervals into one to diminish storage requirements, but still preserving stability. A number of numerical examples illustrate the main points of the paper.

Reviewer: V.Pereyra
65L10Boundary value problems for ODE (numerical methods)
65L50Mesh generation and refinement (ODE)
34B05Linear boundary value problems for ODE