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)
New embedded pairs of explicit Runge-Kutta methods with FSAL properties adapted to the numerical integration of oscillatory problems. (English) Zbl 1225.65072
Summary: A higher order Runge-Kutta (pair) method specially adapted to the numerical integration of IVPs with oscillatory solutions is presented. This method is based on the adapted methods proposed by {\it J.M. Franco} [Appl. Numer. Math. 50, No. 3-4, 427--443 (2004; Zbl 1057.65043)]). We give explicit method (up to order 5) as well as pairs of embedded Runge-Kutta methods of order 5 and 4 designed using the FSAL properties. The stability of the new methods is analyzed. The numerical experiments are carried out to show the efficiency and robustness of our methods in comparison with some efficient methods.

65L05Initial value problems for ODE (numerical methods)
65L06Multistep, Runge-Kutta, and extrapolation methods
Full Text: DOI
[1] Bettis, D. G.: J. appl. Math. phys. (ZAMP). 30, 699 (1979)
[2] Franco, J. M.: Appl. numer. Math.. 50, 427 (2004)
[3] Hairer, E.; Nørsett, S. P.; Wanner, S. P.: Solving ordinary differential equations I, nonstiff problems. (1993) · Zbl 0789.65048
[4] Butcher, J. C.: The numerical analysis of ordinary differential equations. (2003) · Zbl 1040.65057
[5] Dormand, J. R.; Prince, P. J.: J. comput. Appl. math.. 6, 19 (1980)
[6] Coleman, J. P.; Ixaru, L. G.: IMA J. Numer. anal.. 16, 179 (1996)
[7] Van De Vyver, H.: Comput. phys. Commun.. 173, 115 (2005)
[8] Van Der Houwen, P. J.; Sommeijer, B. P.: SIAM J. Numer. anal.. 24, 595 (1987)
[9] Berghe, G. Vanden; De Meyer, H.; Van Daele, M.; Van Hecke, T.: Comput. phys. Commun.. 123, 7 (1999)
[10] Simos, T. E.: Comput. phys. Commun.. 115, 1 (1998)
[11] Franco, J. M.; Palacios, M.: J. comput. Appl. math.. 30, 1 (1990)
[12] Van De Vyver, H.: Phys. lett. A. 352, 278 (2006) · Zbl 1196.37122
[13] Franco, J. M.: J. comput. Appl. math.. 149, 407 (2002)
[14] Galgani, L.; Giorgilli, A.; Martinoli, A.; Vanzini, S.: Physica D. 59, 334 (1992)