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)
An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions. (English) Zbl 1001.65080
Summary: An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions is developed. Numerical and theoretical results obtained for several well known problems show the efficiency of the new method.

65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A34Nonlinear ODE and systems, general
34C25Periodic solutions of ODE
70M20Orbital mechanics (general mechanics)
Full Text: DOI
[1] Landau, L. D.; Lifshitz, F. M.: Quantum mechanics. (1965) · Zbl 0178.57901
[2] Liboff, R. L.: Introductory quantum mechanics. (1980) · Zbl 0891.00009
[3] Lyche, T.: Chebyshevian multistep methods for ordinary differential equations. Numer. math. 19, 65-75 (1972) · Zbl 0221.65123
[4] Raptis, A. D.; Allison, A. C.: Exponential-Fitting methods for the numerical solution of the Schrödinger equation. Comput. phys. Commun. 14, 1-5 (1978)
[5] Hairer, E.; Norset, S. P.; Wanner, G.: 2nd ed. Solving ordinary differential equations. Solving ordinary differential equations 1 (1993)
[6] Stiefel, E.; Bettis, D. G.: Stabilization of cowell’s method. Numer. math. 13, 154-175 (1969) · Zbl 0219.65062