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)
Homotopy perturbation technique. (English) Zbl 0956.70017
Summary: The homotopy perturbation technique does not depend upon a small parameter in the equation. By the homotopy technique in topology, a homotopy can be constructed with an imbedding parameter $p\in [0,1]$, which is considered as a “small parameter”. Here we give some examples, and demonstrate that the approximations obtained by the proposed method are uniformly vaild not only for small parameters, but also for very large parameters.

70K60General perturbation schemes (nonlinear dynamics)
34A45Theoretical approximation of solutions of ODE
34E10Perturbations, asymptotics (ODE)
Full Text: DOI
[1] Liao, S. J.: An approximate solution technique not depending on small parameters: a special example. Int. J. Non-linear mechanics 30, No. 3, 371-380 (1995) · Zbl 0837.76073
[2] Liao, S. J.: Boundary element method for general nonlinear differential operators. Engineering analysis with boundary element 20, No. 2, 91-99 (1997)
[3] A.H. Nayfeh, Introduction to Perturbation Techniques, Wiley, New York, 1981 · Zbl 0449.34001
[4] C.C. Lin, Mathematics Applied to Deterministic Problems in Natural Sciences, Macmillan, New York, 1974 · Zbl 0286.00003
[5] Y.B. Wang et al., An Introduction to Perturbation Techniques (in Chinese), Shanghai Jiaotong University Press, 1986
[6] He, J. H.: A new approach to nonlinear partial differential equations, communications in nonlinear science and numerical simulation. 2, No. 4, 230-235 (1997)
[7] J.H. He, Nonlinear oscillation with fractional derivative and its approximation, International Conference on Vibration Engineering ’98, 1998, Dalian, China