zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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 method for solving fourth-order boundary value problems. (English) Zbl 1144.65311
Summary: We apply the homotopy perturbation method for solving fourth-order boundary value problems. The analytical results of the boundary value problems are obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of the method. The homotopy method can be considered an alternative method to the Adomian decomposition method and its variant forms.

MSC:
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
65H20Global numerical methods for nonlinear algebraic equations, including homotopy approaches
WorldCat.org
Full Text: DOI EuDML
References:
[1] A. H. Nayfeh, Introduction to Perturbation Techniques, John Wiley & Sons, New York, 1981. · Zbl 0449.34001
[2] A. H. Nayfeh, Problems in Perturbation, John Wiley & Sons, New York, 1985. · Zbl 0573.34001
[3] S. J. Liao, “An approximate solution technique not depending on small parameters: a special example,” International Journal of Non-Linear Mechanics, vol. 30, no. 3, pp. 371-380, 1995. · Zbl 0837.76073 · doi:10.1016/0020-7462(94)00054-E
[4] S. J. Liao, “Boundary element method for general nonlinear differential operators,” Engineering Analysis with Boundary Elements, vol. 20, no. 2, pp. 91-99, 1997. · doi:10.1016/S0955-7997(97)00043-X
[5] J.-H. He, “Approximate solution for nonlinear differential equations with convolution product nonlinearities,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 69-73, 1998. · Zbl 0932.65143 · doi:10.1016/S0045-7825(98)00109-1
[6] J.-H. He, “Variational iteration method: a kind of nonlinear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699-708, 1999. · Zbl 05137891 · doi:10.1016/S0020-7462(98)00048-1
[7] J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141-1199, 2006. · Zbl 1102.34039 · doi:10.1142/S0217979206033796
[8] M. A. Noor and S. Tauseef Mohyud-Din, “An efficient method for fourth-order boundary value problems,” to appear in Computers & Mathematics with Applications. · Zbl 1141.65375 · doi:10.1016/j.camwa.2006.12.057
[9] M. A. Noor and S. Tauseef Mohyud-Din, “An efficient algorithm for solving fifth-order boundary value problems,” to appear in Mathematical and Computer Modelling. · Zbl 1133.65052 · doi:10.1016/j.mcm.2006.09.004
[10] M. M. Chawla and C. P. Katti, “Finite difference methods for two-point boundary value problems involving high order differential equations,” BIT, vol. 19, no. 1, pp. 27-33, 1979. · Zbl 0401.65053 · doi:10.1007/BF01931218
[11] E. J. Doedel, “Finite difference collocation methods for nonlinear two-point boundary value problems,” SIAM Journal on Numerical Analysis, vol. 16, no. 2, pp. 173-185, 1979. · Zbl 0438.65068 · doi:10.1137/0716013
[12] T. F. Ma and J. da Silva, “Iterative solutions for a beam equation with nonlinear boundary conditions of third order,” Applied Mathematics and Computation, vol. 159, no. 1, pp. 11-18, 2004. · Zbl 1095.74018 · doi:10.1016/j.amc.2003.08.088