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)
Predictor-corrector methods for periodic second-order initial-value problems. (English) Zbl 0631.65074
This paper deals with the numerical solution of initial value problems for the special second order equation $y''=f(t,y)$, by means of predictor-corrector methods. The authors define the phase lag with respect to the homogeneous solution component as the phase error introduced by the numerical scheme when applied to the test equation $y''=-k\sp 2y$. Thus some predictor-corrector methods introduced by the authors [ibid. 3, 417-437 (1983; Zbl 0533.65045)] for first order differential equations are modified to make them applicable to special second order equations and the coefficients are chosen satisfying the requirement that both the algebraic and phase lag orders be as large as possible. In this way several numerical predictor-corrector schemes with orders 4 and 6 and phase lag orders up to 10 are proposed. The paper ends with some numerical experiments comparing the behaviour of these methods and the classical fourth order Runge-Kutta-Nyström (RKN) method. It is concluded that for problems with periodic solutions the proposed schemes are more efficient than the RKN method.
Reviewer: M.Calvo

65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
34C25Periodic solutions of ODE
Full Text: DOI