메뉴 건너뛰기




Volumn 36, Issue 1, 2008, Pages 53-65

Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL TRANSFORMATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; TIME VARYING SYSTEMS;

EID: 35348853810     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.06.040     Document Type: Article
Times cited : (127)

References (47)
  • 1
    • 0021504145 scopus 로고
    • Convergent series solution of nonlinear equation
    • Adomian G. Convergent series solution of nonlinear equation. J Comput Appl Math 11 (1984) 113-117
    • (1984) J Comput Appl Math , vol.11 , pp. 113-117
    • Adomian, G.1
  • 2
    • 0001422946 scopus 로고
    • Solutions of nonlinear PDE
    • Adomian G. Solutions of nonlinear PDE. Appl Math Lett 11 (1989) 121-123
    • (1989) Appl Math Lett , vol.11 , pp. 121-123
    • Adomian, G.1
  • 3
    • 35348902278 scopus 로고    scopus 로고
    • Adomian G. Solving Frontier problems of physics, The decomposition method, Boston, 1994.
  • 4
    • 0002095007 scopus 로고
    • Noise terms in decomposition solution series
    • Adomian G., and Rach R. Noise terms in decomposition solution series. Comput Math Appl 11 (1992) 61-64
    • (1992) Comput Math Appl , vol.11 , pp. 61-64
    • Adomian, G.1    Rach, R.2
  • 5
    • 0003280712 scopus 로고
    • Equality of partial solutions in the decomposition method for linear and nonlinear partial differential equations
    • Adomian G., and Rach R. Equality of partial solutions in the decomposition method for linear and nonlinear partial differential equations. Appl Math Comput 19 (1990) 9-12
    • (1990) Appl Math Comput , vol.19 , pp. 9-12
    • Adomian, G.1    Rach, R.2
  • 6
    • 0000004102 scopus 로고
    • Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition
    • Adomian G., and Rach R. Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition. J Appl Math 174 (1993) 118-137
    • (1993) J Appl Math , vol.174 , pp. 118-137
    • Adomian, G.1    Rach, R.2
  • 7
    • 43949158252 scopus 로고
    • Convergence of Adomian's method applied to nonlinear equations
    • Abbaoui A., and Cherruauit Y. Convergence of Adomian's method applied to nonlinear equations. Math Comput Model 20 (1994) 69-73
    • (1994) Math Comput Model , vol.20 , pp. 69-73
    • Abbaoui, A.1    Cherruauit, Y.2
  • 8
    • 43949159125 scopus 로고
    • Convergence of Adomian's method applied to differential equations
    • Abbaoui A., and Cherruauit Y. Convergence of Adomian's method applied to differential equations. Math Comput Model 28 (1994) 103-109
    • (1994) Math Comput Model , vol.28 , pp. 103-109
    • Abbaoui, A.1    Cherruauit, Y.2
  • 9
    • 0037054950 scopus 로고    scopus 로고
    • Different applications for the differential transformation in the differential equations
    • Abdel-Halim Hassan I.H. Different applications for the differential transformation in the differential equations. Appl Math Comput 129 (2002) 183-201
    • (2002) Appl Math Comput , vol.129 , pp. 183-201
    • Abdel-Halim Hassan, I.H.1
  • 10
    • 0037170713 scopus 로고    scopus 로고
    • On solving some eigenvalue problems by using a differential transformation
    • Abdel-Halim Hassan I.H. On solving some eigenvalue problems by using a differential transformation. Appl Math Comput 127 (2002) 1-22
    • (2002) Appl Math Comput , vol.127 , pp. 1-22
    • Abdel-Halim Hassan, I.H.1
  • 11
    • 2942717177 scopus 로고    scopus 로고
    • Differential transformation technique for solving higher-order initial value problems
    • Abdel-Halim Hassan I.H. Differential transformation technique for solving higher-order initial value problems. Appl Math Comput 154 (2004) 299-311
    • (2004) Appl Math Comput , vol.154 , pp. 299-311
    • Abdel-Halim Hassan, I.H.1
  • 12
    • 0141961581 scopus 로고    scopus 로고
    • Solution of the system of differential equations by differential transform method
    • Ayaz F. Solution of the system of differential equations by differential transform method. Appl Math Comput 147 (2004) 547-567
    • (2004) Appl Math Comput , vol.147 , pp. 547-567
    • Ayaz, F.1
  • 13
    • 0037507436 scopus 로고    scopus 로고
    • On two-dimensional differential transform method
    • Ayaz F. On two-dimensional differential transform method. Appl Math Comput 143 (2003) 361-374
    • (2003) Appl Math Comput , vol.143 , pp. 361-374
    • Ayaz, F.1
  • 14
    • 33745859755 scopus 로고    scopus 로고
    • A numerical solution of Blasius equation by Adomian's decomposition method and comparison with homotopy perturbation method
    • Abbasbandy S. A numerical solution of Blasius equation by Adomian's decomposition method and comparison with homotopy perturbation method. Chaos, Solitons & Fractals 31 (2007) 257-260
    • (2007) Chaos, Solitons & Fractals , vol.31 , pp. 257-260
    • Abbasbandy, S.1
  • 15
    • 85126468532 scopus 로고    scopus 로고
    • 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.
  • 16
  • 17
    • 0141920794 scopus 로고    scopus 로고
    • Solution of the system of ordinary differential equations by Adomian decomposition method
    • Biazar J., Babolian E., and Islam R. Solution of the system of ordinary differential equations by Adomian decomposition method. Appl Math Comput 147 (2004) 713-719
    • (2004) Appl Math Comput , vol.147 , pp. 713-719
    • Biazar, J.1    Babolian, E.2    Islam, R.3
  • 18
    • 13544264421 scopus 로고    scopus 로고
    • The solution of two-dimensional nonlinear differential equation by Adomian decomposition method
    • Bildik N., and Bayramoglu H. The solution of two-dimensional nonlinear differential equation by Adomian decomposition method. Appl Math Comput 163 (2005) 519-524
    • (2005) Appl Math Comput , vol.163 , pp. 519-524
    • Bildik, N.1    Bayramoglu, H.2
  • 19
    • 0036778809 scopus 로고    scopus 로고
    • Solution of nonlinear equations by modified Adomian decomposition method
    • Babolian E., and Biazar J. Solution of nonlinear equations by modified Adomian decomposition method. Appl Math Comput 132 (2002) 167-172
    • (2002) Appl Math Comput , vol.132 , pp. 167-172
    • Babolian, E.1    Biazar, J.2
  • 20
    • 0006035689 scopus 로고    scopus 로고
    • Solving partial differential equation by differential transformation
    • Chen C.K., and Ho S.H. Solving partial differential equation by differential transformation. Appl Math Comput 106 (1999) 171-179
    • (1999) Appl Math Comput , vol.106 , pp. 171-179
    • Chen, C.K.1    Ho, S.H.2
  • 21
    • 0002261017 scopus 로고    scopus 로고
    • Application of differential transformation to eigenvalue problems
    • Chen C.K., and Ho S.H. Application of differential transformation to eigenvalue problems. Appl Math Comput 79 (1996) 173-188
    • (1996) Appl Math Comput , vol.79 , pp. 173-188
    • Chen, C.K.1    Ho, S.H.2
  • 22
    • 0032345440 scopus 로고    scopus 로고
    • Solution of two point boundary value problems using the differential transformation method
    • Chen C.L., and Liu Y.C. Solution of two point boundary value problems using the differential transformation method. J Opt Theory Appl 99 (1998) 23-35
    • (1998) J Opt Theory Appl , vol.99 , pp. 23-35
    • Chen, C.L.1    Liu, Y.C.2
  • 23
    • 18844365155 scopus 로고    scopus 로고
    • The use of Adomian decomposition method for solving the regularized long-wave equation
    • El-Danaf T.S., Ramadan M.A., and Abd Alaal F.E.I. The use of Adomian decomposition method for solving the regularized long-wave equation. Chaos, Solitons & Fractals 26 (2005) 747-757
    • (2005) Chaos, Solitons & Fractals , vol.26 , pp. 747-757
    • El-Danaf, T.S.1    Ramadan, M.A.2    Abd Alaal, F.E.I.3
  • 24
    • 0038577058 scopus 로고    scopus 로고
    • The decomposition method for studying the Klein-Gordon equation
    • El-Sayed S.M. The decomposition method for studying the Klein-Gordon equation. Chaos, Solitons & Fractals 18 (2003) 1025-1030
    • (2003) Chaos, Solitons & Fractals , vol.18 , pp. 1025-1030
    • El-Sayed, S.M.1
  • 25
    • 27144554011 scopus 로고    scopus 로고
    • A comparison between two different methods for solving KdV-Burgers equation
    • Helal M.A., and Mehanna M.S. A comparison between two different methods for solving KdV-Burgers equation. Chaos, Solitons & Fractals 28 (2006) 320-326
    • (2006) Chaos, Solitons & Fractals , vol.28 , pp. 320-326
    • Helal, M.A.1    Mehanna, M.S.2
  • 27
    • 0035877251 scopus 로고    scopus 로고
    • Two-dimensional differential transform for partial differential equations
    • Jang M.J., Chen C.L., and Liu Y.C. Two-dimensional differential transform for partial differential equations. Appl Math Comput 121 (2001) 261-270
    • (2001) Appl Math Comput , vol.121 , pp. 261-270
    • Jang, M.J.1    Chen, C.L.2    Liu, Y.C.3
  • 28
    • 0000443213 scopus 로고    scopus 로고
    • On solving the initial value problems using the differential transformation method
    • Jang M.J., Chen C.L., and Liu Y.C. On solving the initial value problems using the differential transformation method. Appl Math Comput 115 (2000) 145-160
    • (2000) Appl Math Comput , vol.115 , pp. 145-160
    • Jang, M.J.1    Chen, C.L.2    Liu, Y.C.3
  • 29
    • 0012135963 scopus 로고    scopus 로고
    • Analysis of the response of a strongly nonlinear damped system using a differential transformation technique
    • Jang M.J., Chen C.L., and Liu Y.C. Analysis of the response of a strongly nonlinear damped system using a differential transformation technique. Appl Math Comput 88 (1997) 137-151
    • (1997) Appl Math Comput , vol.88 , pp. 137-151
    • Jang, M.J.1    Chen, C.L.2    Liu, Y.C.3
  • 30
    • 27844437049 scopus 로고    scopus 로고
    • n-Dimensional differential transformation method for solving linear and nonlinear PDE's
    • Kurnaz A., Oturnaz G., and Kiris M.E. n-Dimensional differential transformation method for solving linear and nonlinear PDE's. Int J Comput Math 82 (2005) 369-380
    • (2005) Int J Comput Math , vol.82 , pp. 369-380
    • Kurnaz, A.1    Oturnaz, G.2    Kiris, M.E.3
  • 31
    • 33746022675 scopus 로고    scopus 로고
    • Decomposition method for the Camassa-Holm equation
    • Kamdem J.S., and Qiao Z. Decomposition method for the Camassa-Holm equation. Chaos, Solitons & Fractals 11 (2007) 437-447
    • (2007) Chaos, Solitons & Fractals , vol.11 , pp. 437-447
    • Kamdem, J.S.1    Qiao, Z.2
  • 32
    • 0037411749 scopus 로고    scopus 로고
    • An application of the decomposition method for the generalized KdV and RLW equations
    • Kaya D., and El-Sayed S.M. An application of the decomposition method for the generalized KdV and RLW equations. Chaos, Solitons & Fractals 17 (2003) 869-877
    • (2003) Chaos, Solitons & Fractals , vol.17 , pp. 869-877
    • Kaya, D.1    El-Sayed, S.M.2
  • 33
    • 27644504642 scopus 로고    scopus 로고
    • Blow-up solutions obtained using the decomposition method
    • Lesnic D. Blow-up solutions obtained using the decomposition method. Chaos, Solitons & Fractals 28 (2006) 776-787
    • (2006) Chaos, Solitons & Fractals , vol.28 , pp. 776-787
    • Lesnic, D.1
  • 35
    • 85126464242 scopus 로고    scopus 로고
    • 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.
  • 36
    • 12444296497 scopus 로고    scopus 로고
    • An application for linear and nonlinear heat equations by Adomian's decomposition method
    • Pamuk S. An application for linear and nonlinear heat equations by Adomian's decomposition method. Appl Math Comput 163 (2005) 89-96
    • (2005) Appl Math Comput , vol.163 , pp. 89-96
    • Pamuk, S.1
  • 37
    • 10444220985 scopus 로고    scopus 로고
    • Solution of linear and nonlinear parabolic equations by the decomposition method
    • Soufyane A., and Boulmalf M. Solution of linear and nonlinear parabolic equations by the decomposition method. Appl Math Comput 162 (2005) 687-693
    • (2005) Appl Math Comput , vol.162 , pp. 687-693
    • Soufyane, A.1    Boulmalf, M.2
  • 38
    • 0000013352 scopus 로고    scopus 로고
    • The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model
    • Wazwaz A.M. The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model. Appl Math Comput 110 (2000) 251-264
    • (2000) Appl Math Comput , vol.110 , pp. 251-264
    • Wazwaz, A.M.1
  • 39
    • 0002566545 scopus 로고    scopus 로고
    • A comparison between Adomian decomposition method and Taylor series method in the series solutions
    • Wazwaz A.M. A comparison between Adomian decomposition method and Taylor series method in the series solutions. Appl Math Comput 97 (1998) 37-44
    • (1998) Appl Math Comput , vol.97 , pp. 37-44
    • Wazwaz, A.M.1
  • 40
    • 0035840358 scopus 로고    scopus 로고
    • Exact solution to nonlinear diffusion equations obtained by the decomposition method
    • Wazwaz A.M. Exact solution to nonlinear diffusion equations obtained by the decomposition method. Appl Math Comput 123 (2001) 109-122
    • (2001) Appl Math Comput , vol.123 , pp. 109-122
    • Wazwaz, A.M.1
  • 41
    • 0000937070 scopus 로고    scopus 로고
    • Necessary conditions for the appearance of noise term in decomposition solution series
    • Wazwaz A.M. Necessary conditions for the appearance of noise term in decomposition solution series. J Math Anal Appl 5 (1997) 265-274
    • (1997) J Math Anal Appl , vol.5 , pp. 265-274
    • Wazwaz, A.M.1
  • 42
    • 0035452509 scopus 로고    scopus 로고
    • Construction of solitary wave solutions and rational solutions for KdV equation by Adomian decomposition method
    • Wazwaz A.M. Construction of solitary wave solutions and rational solutions for KdV equation by Adomian decomposition method. Chaos, Solitons & Fractals 12 (2001) 2283-2293
    • (2001) Chaos, Solitons & Fractals , vol.12 , pp. 2283-2293
    • Wazwaz, A.M.1
  • 43
    • 0035372279 scopus 로고    scopus 로고
    • Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method
    • Wazwaz A.M. Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method. Chaos, Solitons & Fractals 12 (2001) 1549-1556
    • (2001) Chaos, Solitons & Fractals , vol.12 , pp. 1549-1556
    • Wazwaz, A.M.1
  • 44
    • 85126461097 scopus 로고    scopus 로고
    • 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.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.