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)
Variational iteration method for solving wave equation. (English) Zbl 1165.65396
Summary: By the variational iteration method the solution of the wave equation in different forms is exactly obtained. The obtained solutions show that the variational iteration method is effective, simple and easy compared with many of the other methods. So it has a wide range of applications in physical and mathematical problems, linear and nonlinear as well.
MSC:
65M99Numerical methods for IVP of PDE
35Q35PDEs in connection with fluid mechanics
References:
[1]Anderson, D. A.; Tannehill, J. C.; Pletcher, R. H.: Computational fluid mechanics and heat transfer, (1984) · Zbl 0569.76001
[2]He, J. H.: A new approach to nonlinear partial differential equations, Commun. non-linear sci. Numer. simul. 2, No. 4, 230-235 (1997) · Zbl 0923.35046 · doi:10.1016/S1007-5704(97)90029-0
[3]He, J. H.: Variational iteration method for delay differential equations, Commun. non-linear sci. Numer. simul. 2, No. 4, 235-236 (1997) · Zbl 0924.34063
[4]J.H. He, Non-linear oscillation with fractional derivative and its approximation, Int. conf. on Vibration Engineering 98, Dalian, China, (1998)
[5]He, J. H.: Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. methods appl. Mech. engrg. 167, 57-68 (1998) · Zbl 0942.76077 · doi:10.1016/S0045-7825(98)00108-X
[6]He, J. H.: Variational iteration method - a kind of non-linear analytical technique: some examples, Internat. J. Non-linear mech. 34, 699-708 (1999)
[7]He, J. H.: Variational iteration method for autonomous ordinary differential systems, Appl. math. Comput. 114, 115-123 (2000) · Zbl 1027.34009 · doi:10.1016/S0096-3003(99)00104-6
[8]Abdou, M. A.; Soliman, A. A.: Variational iteration method for solving burger’s and coupled burger’s equations, J. comput. Appl. math. 181, No. 2, 245-251 (2005) · Zbl 1072.65127 · doi:10.1016/j.cam.2004.11.032
[9]He, J. H.; Wu, X. H.: Chaos solitons fractals, Chaos solitons fractals 29, No. 1, 108 (2006)
[10]Inokuti, M.: General use of the Lagrange multiplier in non-linear mathematical physics, Variational method in the mechanics of solids, 156-162 (1978)
[11]He, J. H.: Semi-inverse method of establishing generalized principles for fluid mechanics with emphasis on turbomachinery aerodynamics, Int. J. Turbo jet-eng. 14, No. 1, 23-28 (1997)
[12]He, J. H.: Comput. methods, appl. Mech. eng., Comput. methods, appl. Mech. eng. 167, 69-73 (1998)
[13]He, J. H.: Variational iteration method for non-linearity and its applications, Mechanics and practice 20, No. 1, 30-32 (1998)
[14]He, J. H.: Variational iteration approach to 2-spring system, Mech. sci. Technol. 17, No. 2, 221-223 (1998)
[15]Abulwafa, E. M.; Abdou, M. A.; Mahmoud, A. A.: The solution of nonlinear coagulation problem with mass loss, Chaos solitons fractals 29, 313-330 (2006) · Zbl 1101.82018 · doi:10.1016/j.chaos.2005.08.044
[16]Abdou, M. A.: On the variational iteration method, Phys. lett. A 366, 61 (2007) · Zbl 1203.65205 · doi:10.1016/j.physleta.2007.01.073
[17]Abulwafa, E. M.; Abdou, M. A.; Mahmoud, A. A.: Nonlinear fluid flows in pipe-like domain problem using variational iteration method, Chaos solitons fractals 32, 1384-1397 (2007) · Zbl 1128.76019 · doi:10.1016/j.chaos.2005.11.050
[18]Abulwafa, E. M.; Abdou, M. A.; Mahmoud, A. A.: Variational iteration method to solve nonlinear Boltzmann equation, Z. nat. Forsch. 63a, 131-139 (2008)
[19]El-Wakil, S. A.; Abulwafa, E. M.; Abdou, M. A.: Improved variational iteration method for solving coupled KdV and Boussinesq-like B(m,n) equations, Chaos solitons fractals (2008)
[20]El-Wakil, S. A.; Abdou, M. A.: New applications of variational iteration method using Adomian polynomials, Int. J. Of nonlinear dynam. 52, No. 1–2, 41-49 (2008) · Zbl 1170.76356 · doi:10.1007/s11071-007-9256-8
[21]Hemeda, A. A.: Variational iteration method for solving non-linear partial differential equations, Chaos solitons fractals (2008)