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)
Extracting a general iterative method from an Adomian decomposition method and comparing it to the variational iteration method. (English) Zbl 1189.65245
Summary: A new form of Adomian decomposition method (ADM) is presented; by this form a general iterative method can be achieved in which there is no need of calculating Adomian polynomials. Also, this general iterative method is compared with the Adomian decomposition method and variational iteration method (VIM) and its advantages are expressed.
65M99Numerical methods for IVP of PDE
[1]Adomian, G.: A review of the decomposition method in applied mathematics, J. math. Anal. appl. 135, 501-544 (1988) · Zbl 0671.34053 · doi:10.1016/0022-247X(88)90170-9
[2]Adomian, G.: Solving frontier problems of physics: the decomposition method, (1994)
[3]He, J. H.: A new approach to nonlinear partial differential equations, Commun. nonlinear sci. Numer. simul. 2, No. 4, 203-205 (1997) · Zbl 0923.35046 · doi:10.1016/S1007-5704(97)90029-0
[4]He, J. H.: Variational iteration method–A kind of nonlinear analytical technique: some examples, Internat. J. Non-linear mech. 34, 708-799 (1999)
[5]He, J. H.: A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Internat. J. Non-linear mech. 35, No. 1, 37-43 (2000) · Zbl 1068.74618 · doi:10.1016/S0020-7462(98)00085-7
[6]He, J. H.: New interpretation of homotopy-perturbation method, Internat. J. Modern phys. B 20, No. 18, 2561-2568 (2006)
[7]He, J. H.; Wu, Xu-Hong: Exp-function method for nonlinear wave equations, Chaos solitons fractals 30, No. 3, 700-708 (2006) · Zbl 1141.35448 · doi:10.1016/j.chaos.2006.03.020
[8]He, J. H.; Abdou, M. A.: New periodic solutions for nonlinear evolution equations using exp-function method, Chaos solitons fractals 34, 1421-1429 (2007) · Zbl 1152.35441 · doi:10.1016/j.chaos.2006.05.072
[9]He, J. H.: Some asymptotic methods for strongly nonlinear equations, Internat. J. Modern phys. B 20, No. 10, 1141-1199 (2006) · Zbl 1102.34039 · doi:10.1142/S0217979206033796
[10]J.H. He, Non-perturbative methods for strongly nonlinear problems. Berlin: Dissertation. de-Verlag in Internet GmbH., 2006
[11]Ismail, N. A.; Raslan, K.; Rabboh, A. Abd: Adomian decomposition method for burger’s–Huxley and burger’s–Fisher equations, Appl. math. Comput. 159, 291-301 (2004) · Zbl 1062.65110 · doi:10.1016/j.amc.2003.10.050
[12]Biazar, J.: Solution of systems of integral–differential equations by Adomian decomposition method, Appl. math. Comput. 168, 1232-1238 (2005) · Zbl 1082.65594 · doi:10.1016/j.amc.2004.10.015
[13]Biazar, J.; Islam, R.: Solution of wave equaton by Adomian decomposition method and the restrictions of the method, Appl. math. Comput. 149, 807-814 (2004) · Zbl 1038.65100 · doi:10.1016/S0096-3003(03)00186-3
[14]Wazwaz, A. M.: Adomian decomposition method for a reliable treatment of the bratu-type equations, Appl. math. Comput. 166, 652-663 (2005) · Zbl 1073.65068 · doi:10.1016/j.amc.2004.06.059
[15]Biazar, J.; Ebrahimi, H.: An approximation to the solution of hyperbolic equations by Adomian decomposition method and comparison with charactistics method, Appl. math. Comput. 163, 633-638 (2005) · Zbl 1060.65651 · doi:10.1016/j.amc.2004.04.005
[16]Wazwaz, A. M.: A comparison between the variational iteration method and Adomian decomposition method, J. comput. Appl. math. 207, 129-136 (2007) · Zbl 1119.65103 · doi:10.1016/j.cam.2006.07.018
[17]Babolian, E.; Biazar, J.: On the order of convergence of Adomian method, Appl. math. Comput. 130, 383-387 (2002) · Zbl 1044.65043 · doi:10.1016/S0096-3003(01)00103-5
[18]He, J. H.: Variational iteration method for delay differential equations, Commun. nonlinear sci. Numer. simul., 235-236 (1997)
[19]Shakeri, F.; Dehghan, M.: Solution of a model describing biological species living together using the variational iteration method, Math. comput. Modelling 48, 685-699 (2008) · Zbl 1156.92332 · doi:10.1016/j.mcm.2007.11.012
[20]Biazar, J.; Ghazvini, H.: He’s variational iteration method for fourth-order parabolic equations, Comput. math. Appl. (2006)
[21]Wazwaz, A. M.: The variational iteration method for rational solutions for KdV, K (2,2), Burgers, and cubic Boussinesq equations, J. comput. Appl. math. 207, 18-23 (2007) · Zbl 1119.65102 · doi:10.1016/j.cam.2006.07.010
[22]Abdou, M. A.; Soliman, A.: Variational iteration method for solving burger’s and coupled burger’s equations, J. comput. Appl. math. 181, 245-251 (2005) · Zbl 1072.65127 · doi:10.1016/j.cam.2004.11.032
[23]Momani, S.; Abuasad, S.: Application of he’s variational iteration method to Helmholtz equation, Chaos solitons fractals 27, 1119-1123 (2006) · Zbl 1086.65113 · doi:10.1016/j.chaos.2005.04.113
[24]Tatari, M.; Dehghan, M.: On the convergence of he’s variational iteration method, J. comput. Appl. math. 207, 121-128 (2007) · Zbl 1120.65112 · doi:10.1016/j.cam.2006.07.017
[25]Wazwaz, A. M.: The variational iteration method for solving two forms of Blasius equation on a half-infinite domain, Appl. math. Comput. 188, 485-491 (2007) · Zbl 1114.76055 · doi:10.1016/j.amc.2006.10.009