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)
Comparison differential transformation technique with adomian decomposition method for linear and nonlinear initial value problems. (English) Zbl 1152.65474

MSC:
65M99Numerical methods for IVP of PDE
WorldCat.org
Full Text: DOI
References:
[1] Adomian, G.: Convergent series solution of nonlinear equation, J comput appl math 11, 113-117 (1984) · Zbl 0549.65034 · doi:10.1016/0377-0427(84)90022-0
[2] Adomian, G.: Solutions of nonlinear PDE, Appl math lett 11, 121-123 (1989) · Zbl 0933.65121 · doi:10.1016/S0893-9659(98)00043-3
[3] Adomian G. Solving Frontier problems of physics, The decomposition method, Boston, 1994. · Zbl 0802.65122
[4] 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
[5] Adomian, G.; Rach, R.: Equality of partial solutions in the decomposition method for linear and nonlinear partial differential equations, Appl math comput 19, 9-12 (1990) · Zbl 0702.35058 · doi:10.1016/0898-1221(90)90246-G
[6] Adomian, G.; Rach, R.: Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition, J appl math 174, 118-137 (1993) · Zbl 0796.35017 · doi:10.1006/jmaa.1993.1105
[7] Abbaoui, A.; Cherruauit, Y.: Convergence of Adomian’s method applied to nonlinear equations, Math comput model 20, 69-73 (1994) · Zbl 0822.65027 · doi:10.1016/0895-7177(94)00163-4
[8] Abbaoui, A.; Cherruauit, Y.: Convergence of Adomian’s method applied to differential equations, Math comput model 28, 103-109 (1994) · Zbl 0809.65073 · doi:10.1016/0898-1221(94)00144-8
[9] Hassan, I. H. Abdel-Halim: Different applications for the differential transformation in the differential equations, Appl math comput 129, 183-201 (2002) · Zbl 1026.34010 · doi:10.1016/S0096-3003(01)00037-6
[10] Hassan, I. H. Abdel-Halim: On solving some eigenvalue problems by using a differential transformation, Appl math comput 127, 1-22 (2002) · Zbl 1030.34028 · doi:10.1016/S0096-3003(00)00123-5
[11] Hassan, I. H. Abdel-Halim: Differential transformation technique for solving higher-order initial value problems, Appl math comput 154, 299-311 (2004) · Zbl 1054.65069 · doi:10.1016/S0096-3003(03)00708-2
[12] Ayaz, F.: Solution of the system of differential equations by differential transform method, Appl math comput 147, 547-567 (2004) · Zbl 1032.35011 · doi:10.1016/S0096-3003(02)00794-4
[13] Ayaz, F.: On two-dimensional differential transform method, Appl math comput 143, 361-374 (2003) · Zbl 1023.35005 · doi:10.1016/S0096-3003(02)00368-5
[14] Abbasbandy, S.: A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method, Chaos, solitons & fractals 31, 257-260 (2007)
[15] Abassy TA, El-Tawil MA, Saleh Hk. The solution of Burger’s and good Boussinesq equations using ADM-Padé technique. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.11.029. · Zbl 1130.35111 · doi:10.1016/j.chaos.2005.11.029
[16] 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
[17] Biazar, J.; Babolian, E.; Islam, R.: Solution of the system of ordinary differential equations by Adomian decomposition method, Appl math comput 147, 713-719 (2004) · Zbl 1034.65053 · doi:10.1016/S0096-3003(02)00806-8
[18] Bildik, N.; Bayramoglu, H.: The solution of two-dimensional nonlinear differential equation by Adomian decomposition method, Appl math comput 163, 519-524 (2005) · Zbl 1067.65106 · doi:10.1016/j.amc.2004.03.029
[19] Babolian, E.; Biazar, J.: Solution of nonlinear equations by modified Adomian decomposition method, Appl math comput 132, 167-172 (2002) · Zbl 1023.65040 · doi:10.1016/S0096-3003(01)00184-9
[20] Chen, C. K.; Ho, S. H.: Solving partial differential equation by differential transformation, Appl math comput 106, 171-179 (1999) · Zbl 1028.35008
[21] Chen, C. K.; Ho, S. H.: Application of differential transformation to eigenvalue problems, Appl math comput 79, 173-188 (1996) · Zbl 0879.34077 · doi:10.1016/0096-3003(95)00253-7
[22] Chen, C. L.; Liu, Y. C.: Solution of two point boundary value problems using the differential transformation method, J opt theory appl 99, 23-35 (1998) · Zbl 0935.65079 · doi:10.1023/A:1021791909142
[23] El-Danaf, T. S.; Ramadan, M. A.; Alaal, F. E. I. Abd: The use of Adomian decomposition method for solving the regularized long-wave equation, Chaos, solitons & fractals 26, 747-757 (2005) · Zbl 1073.35010 · doi:10.1016/j.chaos.2005.02.012
[24] El-Sayed, S. M.: The decomposition method for studying the Klein -- Gordon equation, Chaos, solitons & fractals 18, 1025-1030 (2003) · Zbl 1068.35069 · doi:10.1016/S0960-0779(02)00647-1
[25] Helal, M. A.; Mehanna, M. S.: A comparison between two different methods for solving KdV -- Burgers equation, Chaos, solitons & fractals 28, 320-326 (2006) · Zbl 1084.65079 · doi:10.1016/j.chaos.2005.06.005
[26] Hashim, I.; Noorani, M. S. M.; Ahmad, R.; Bakar, S. A.; Ismail, E. S.; Zakaria, A. M.: Accuracy of the decomposition method applied to the Lorenz system, Chaos, solitons & fractals 28, 1149-1158 (2006) · Zbl 1096.65066
[27] Jang, M. J.; Chen, C. L.; Liu, Y. C.: Two-dimensional differential transform for partial differential equations, Appl math comput 121, 261-270 (2001) · Zbl 1024.65093 · doi:10.1016/S0096-3003(99)00293-3
[28] Jang, M. J.; Chen, C. L.; Liu, Y. C.: On solving the initial value problems using the differential transformation method, Appl math comput 115, 145-160 (2000) · Zbl 1023.65065 · doi:10.1016/S0096-3003(99)00137-X
[29] Jang, M. J.; Chen, C. L.; Liu, Y. C.: Analysis of the response of a strongly nonlinear damped system using a differential transformation technique, Appl math comput 88, 137-151 (1997) · Zbl 0911.65067 · doi:10.1016/S0096-3003(96)00308-6
[30] Kurnaz, A.; Oturnaz, G.; Kiris, M. E.: N-dimensional differential transformation method for solving linear and nonlinear PDE’s, Int J comput math 82, 369-380 (2005) · Zbl 1065.35011
[31] Kamdem, J. S.; Qiao, Z.: Decomposition method for the Camassa-Holm equation, Chaos, solitons & fractals 11, 437-447 (2007) · Zbl 1138.35396
[32] Kaya, D.; El-Sayed, S. M.: An application of the decomposition method for the generalized KdV and RLW equations, Chaos, solitons & fractals 17, 869-877 (2003) · Zbl 1030.35139 · doi:10.1016/S0960-0779(02)00569-6
[33] Lesnic, D.: Blow-up solutions obtained using the decomposition method, Chaos, solitons & fractals 28, 776-787 (2006) · Zbl 1109.35024 · doi:10.1016/j.chaos.2005.08.003
[34] Myint-U, T.: Partial differential equations of mathematical physics, (1980) · Zbl 0428.35001
[35] Noorani MSM, Hashim I, Ahmad R, Bakar SA, Ismail ES, Zakaria AM. Comparing numerical methods for the solutions of the Chen system. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.12.036. · Zbl 1131.65101 · doi:10.1016/j.chaos.2005.12.036
[36] Pamuk, S.: An application for linear and nonlinear heat equations by Adomian’s decomposition method, Appl math comput 163, 89-96 (2005) · Zbl 1060.65653 · doi:10.1016/j.amc.2003.10.051
[37] Soufyane, A.; Boulmalf, M.: Solution of linear and nonlinear parabolic equations by the decomposition method, Appl math comput 162, 687-693 (2005) · Zbl 1063.65111 · doi:10.1016/j.amc.2004.01.005
[38] 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
[39] 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
[40] Wazwaz, A. M.: Exact solution to nonlinear diffusion equations obtained by the decomposition method, Appl math comput 123, 109-122 (2001) · Zbl 1027.35019 · doi:10.1016/S0096-3003(00)00064-3
[41] Wazwaz, A. M.: Necessary conditions for the appearance of noise term in decomposition solution series, J math anal appl 5, 265-274 (1997) · Zbl 0882.65132 · doi:10.1016/S0096-3003(95)00327-4
[42] Wazwaz, A. M.: Construction of solitary wave solutions and rational solutions for KdV equation by Adomian decomposition method, Chaos, solitons & fractals 12, 2283-2293 (2001) · Zbl 0992.35092 · doi:10.1016/S0960-0779(00)00188-0
[43] Wazwaz, A. M.: Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method, Chaos, solitons & fractals 12, 1549-1556 (2001) · Zbl 1022.35051 · doi:10.1016/S0960-0779(00)00133-8
[44] Wang Y-y, Dai C-q, Wu L, Zhang J-f. Exact and numerical solitary wave solutions of generalized Zakharov equation by Adomian decomposition method. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.11.071. · Zbl 1130.35120 · doi:10.1016/j.chaos.2005.11.071
[45] Zhou, J. K.: Differential transformation and its application for electrical circuits, (1986)
[46] Zauderer, E.: Partial differential equations of applied mathematics, (1989) · Zbl 0699.35003
[47] Zwillinger, D.: Handbook of differential equations, (1992) · Zbl 0741.34002