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)
Application of the variational iteration method to some nonlinear one-dimensional oscillations. (English) Zbl 1238.70018
From the introduction: In this paper a kind of analytical technique for a general nonlinear problem is presented. The problems are initially approximated with unknown constants, which can be further determined. The iterative process is constructed by a general Lagrange multiplier, which can be identified optimally via variational theory. This method is effective and accurate for nonlinear problems with approximations converging rapidly to accurate solutions.
70K40Forced nonlinear motions (general mechanics)
70-08Computational methods (mechanics of particles and systems)
[1]He J-H (2000) A modified perturbation technique depending upon an artificial parameter. Meccanica 35(4):299–311 · Zbl 0986.70016 · doi:10.1023/A:1010349221054
[2]He J-H (1999) Variational iteration method–a kind of non-linear analytical technique: some examples. Int J Non-Linear Mech 34(4):699–708 · Zbl 05137891 · doi:10.1016/S0020-7462(98)00048-1
[3]Marinca V (2002) An approximate solution for one-dimensional weakly nonlinear oscillations. Int J Nonlinear Sci Num Sim 3:107–120
[4]Gradshteyn IS, Ryzhik IM (1980) Tables of integrals, series and products. Academic Press, New York
[5]Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Willey, New York
[6]He JH (2007) Variational iteration method. Some recent results and new interpretations. J Comp Appl Math 207(1):3–17 · Zbl 1119.65049 · doi:10.1016/j.cam.2006.07.009
[7]Wu B, Li P (2001) A method for obtaining approximate analytic periods for a class of nonlinear oscillators. Meccanica 36(2):167–176 · Zbl 1008.70016 · doi:10.1023/A:1013067311749
[8]Spanos PD, Di Paola M, Failla G (2001) A Galerkin approach for power spectrum determination of nonlinear oscillators. Meccanica 37(1–2):51–65 · Zbl 1060.70031 · doi:10.1023/A:1019610512675
[9]Marinca V, Herişanu N (2006) Periodic solutions of Duffing equation with strong nonlinearity. Chaos Solitons Fractals (2006, in press). doi: 10.1016/j.chaos.2006.08.033