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)
Application of He’s variational iteration method and Adomian’s decomposition method to the fractional KdV-Burgers-Kuramoto equation. (English) Zbl 1189.65255
Summary: The fractional KdV-Burgers-Kuramoto equation is studied. He’s variational iteration method (VIM) and Adomian’s decomposition method (ADM) are applied to obtain its solution. Comparison with HAM is made to highlight the significant features of the employed methods and their capability of handling completely integrable equations.
MSC:
65M99Numerical methods for IVP of PDE
References:
[1]West, B. J.; Bolognab, M.; Grigolini, P.: Physics of fractal operators, (2003)
[2]Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equations, (1993)
[3]Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives: theory and applications, (1993) · Zbl 0818.26003
[4]Podlubny, I.: Fractional differential equations, (1999)
[5]He, J. H.: Int. J. Mod. phys. B, Int. J. Mod. phys. B 20, No. 10, 1141 (2006)
[6]He, J. H.: Non-perturbative methods for strongly nonlinear problems, (2006)
[7]He, J. H.: Comput. methods appl. Mech. engrg., Comput. methods appl. Mech. engrg. 167, 57 (1998)
[8]He, J. H.: Appl. math. Comput., Appl. math. Comput. 114, No. 2/3, 115 (2000)
[9]He, J. H.; Wu, X. H.: Chaos solitons fractals, Chaos solitons fractals 29, No. 1, 108 (2006)
[10]He, J. H.: Commun. nonlinear sci. Numer. simul., Commun. nonlinear sci. Numer. simul. 2, No. 4, 203 (1997)
[11]He, J. H.: Int. J. Nonlinear mech., Int. J. Nonlinear mech. 34, 799 (1999)
[12]He, J. H.: Mech. res. Commun., Mech. res. Commun. 3291, 93 (2005)
[13]He, J. H.: Chaos solitons fractals, Chaos solitons fractals 26, No. 3, 695 (2005)
[14]Ganji, D. D.; Jannatabadi, M.; Mohseni, E.: J. comput. Appl. math., J. comput. Appl. math. 207, No. 1, 35 (2007)
[15]Ganji, D. D.; Sadighi, A.: J. comput. Appl. math., J. comput. Appl. math. (2006)
[16]Ganji, D. D.; Jannatabadi, M.; Mohseni, E.: J. comput. Appl. math., J. comput. Appl. math. (2006)
[17]Tari, Hafez; Ganji, D. D.; Babazadeh, H.: Phys. lett. A, Phys. lett. A 363, No. 3, 213-217 (2007)
[18]Lesnic, D.: Chaos solitons fractals, Chaos solitons fractals 28, 776 (2006)
[19]Adomian, G.: Convergent series solution of nonlinear equation, J. comput. Appl. mat. 11, 113-117 (1984) · Zbl 0549.65034 · doi:10.1016/0377-0427(84)90022-0
[20]Adomian, G.: Solutions of nonlinear PDE, Appl. math. Lett. 11, 121-123 (1989) · Zbl 0933.65121 · doi:10.1016/S0893-9659(98)00043-3
[21]G. Adomian, Solving Frontier Problems of Physics, The Decomposition Method, Boston, 1994
[22]Adomian, G.; Rach, R.: Noise terms in decomposition solution series, Comput. math. Appl. 11, 61-64 (1992) · Zbl 0777.35018 · doi:10.1016/0898-1221(92)90031-C
[23]G. Adomian, R. Rach, Equality of partial solutions in the decomposition method for linear and nonlinear partial differential · Zbl 0702.35058 · doi:10.1016/0898-1221(90)90246-G
[24]Wazwaz, A. M.: The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model, Appl. math. Comput. 110, 251-264 (2000) · Zbl 1023.65109 · doi:10.1016/S0096-3003(99)00131-9
[25]Wazwaz, A. M.: A comparison between Adomian decomposition method and Taylor series method in the series solutions, Appl. math. Comput. 97, 37-44 (1998) · Zbl 0943.65084 · doi:10.1016/S0096-3003(97)10127-8
[26]Wazwaz, A. M.: Exact solution to nonlinear diffusion equations obtained by the decomposition method, Appl. math. Comput. 123, 109-122 (2001)
[27]Song, Lina; Zhang, Hongqing: Application of homotopy analysis method to fractional KdV–Burgers–Kuramoto equation, Phys. lett. A 367, 88-94 (2007) · Zbl 1209.65115 · doi:10.1016/j.physleta.2007.02.083
[28]Caputo, M.: J. roy. Astr. soc., J. roy. Astr. soc. 13, 529 (1967)
[29]Momani, S.; Odibat, Z.: Phys. lett. A, Phys. lett. A 1, No. 53, 1 (2006)
[30]Momani, S.; Abusaad, S.: Chaos solitons fractals, Chaos solitons fractals 27, No. 5, 1119 (2005)