메뉴 건너뛰기




Volumn 37, Issue 3, 2013, Pages 1590-1598

A new improved Adomian decomposition method and its application to fractional differential equations

Author keywords

Approximate solution; Fractional differential equation; Improved Adomian decomposition method

Indexed keywords

ADOMIAN DECOMPOSITION METHOD; ANALYTICAL APPROXIMATE SOLUTION; APPROXIMATE SOLUTION; FRACTIONAL DIFFERENTIAL EQUATIONS; ITERATIVE FORMULAS;

EID: 84870243484     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2012.03.016     Document Type: Article
Times cited : (74)

References (26)
  • 5
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 1998, 167:57-68.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.167 , pp. 57-68
    • He, J.H.1
  • 6
    • 38049021511 scopus 로고    scopus 로고
    • On the solution of the fractional nonlinear Schrödinger equation
    • Rida S.Z., El-Sherbiny H.M., Arafa A.A.M. On the solution of the fractional nonlinear Schrödinger equation. Phys. Lett. A 2008, 372:553-558.
    • (2008) Phys. Lett. A , vol.372 , pp. 553-558
    • Rida, S.Z.1    El-Sherbiny, H.M.2    Arafa, A.A.M.3
  • 7
    • 34548384362 scopus 로고    scopus 로고
    • Numerical methods for nonlinear partial differential equations of fractional order
    • Odibat Z.M., Momani S. Numerical methods for nonlinear partial differential equations of fractional order. Appl. Math. Model. 2008, 32:28-39.
    • (2008) Appl. Math. Model. , vol.32 , pp. 28-39
    • Odibat, Z.M.1    Momani, S.2
  • 8
    • 0037174280 scopus 로고    scopus 로고
    • Analytical approximate solutions for nonlinear fractional differential equations
    • Shawagfeh N.T. Analytical approximate solutions for nonlinear fractional differential equations. Appl. Math. Comput. 2002, 131:517-529.
    • (2002) Appl. Math. Comput. , vol.131 , pp. 517-529
    • Shawagfeh, N.T.1
  • 9
    • 34547661760 scopus 로고    scopus 로고
    • Numerical solutions of fractional Boussinesq equation
    • Wang Q. Numerical solutions of fractional Boussinesq equation. Commun. Theor. Phys. (Beijing, China) 2007, 47:413-420.
    • (2007) Commun. Theor. Phys. (Beijing, China) , vol.47 , pp. 413-420
    • Wang, Q.1
  • 10
    • 65449123574 scopus 로고    scopus 로고
    • Solving the fractional BBM-Burgers equation using the homotopy analysis method
    • Song L.N., Zhang H.Q. Solving the fractional BBM-Burgers equation using the homotopy analysis method. Chaos Soliton Fractals 2009, 40:1616-1622.
    • (2009) Chaos Soliton Fractals , vol.40 , pp. 1616-1622
    • Song, L.N.1    Zhang, H.Q.2
  • 11
    • 43049157795 scopus 로고    scopus 로고
    • Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives
    • Chen Y., An H.L. Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives. Appl. Math. Comput. 2008, 200:87-95.
    • (2008) Appl. Math. Comput. , vol.200 , pp. 87-95
    • Chen, Y.1    An, H.L.2
  • 12
    • 0041185368 scopus 로고
    • A review of the decomposition method in applied mathematics
    • Adomian G. A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 1988, 135:501-544.
    • (1988) J. Math. Anal. Appl. , vol.135 , pp. 501-544
    • Adomian, G.1
  • 14
    • 0347450513 scopus 로고    scopus 로고
    • A new algorithm for calculating Adomian polynomials for nonlinear operators
    • Wazwaz A.M. A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl. Math. Comput. 2000, 111:33-51.
    • (2000) Appl. Math. Comput. , vol.111 , pp. 33-51
    • Wazwaz, A.M.1
  • 15
    • 26844495279 scopus 로고    scopus 로고
    • Extended Newton's method for a system of nonlinear equations by modified Adomian decomposition method
    • Abbasbandy S. Extended Newton's method for a system of nonlinear equations by modified Adomian decomposition method. Appl. Math. Comput. 2005, 170:648-656.
    • (2005) Appl. Math. Comput. , vol.170 , pp. 648-656
    • Abbasbandy, S.1
  • 16
    • 73449134442 scopus 로고    scopus 로고
    • Improved Adomian decomposition method
    • Abassy T.A. Improved Adomian decomposition method. Comput. Math. Appl. 2010, 59:42-54.
    • (2010) Comput. Math. Appl. , vol.59 , pp. 42-54
    • Abassy, T.A.1
  • 17
    • 77955330863 scopus 로고    scopus 로고
    • Approximate rational Jacobi elliptic function solutions of the fractional differential equations via the enhanced Adomian decomposition method
    • Song L.N., Wang W.G. Approximate rational Jacobi elliptic function solutions of the fractional differential equations via the enhanced Adomian decomposition method. Phys. Lett. A 2010, 374:3190-3196.
    • (2010) Phys. Lett. A , vol.374 , pp. 3190-3196
    • Song, L.N.1    Wang, W.G.2
  • 19
    • 55549136027 scopus 로고    scopus 로고
    • Notes on the homotopy analysis method: some definitions and theorems
    • Liao S.J. Notes on the homotopy analysis method: some definitions and theorems. Commun. Nonlinear Sci. Numer. Simulat. 2009, 14:983-997.
    • (2009) Commun. Nonlinear Sci. Numer. Simulat. , vol.14 , pp. 983-997
    • Liao, S.J.1
  • 20
    • 76049117931 scopus 로고    scopus 로고
    • An optimal homotopy-analysis approach for strongly nonlinear differential equations
    • Liao S.J. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simulat. 2010, 15:2003-2016.
    • (2010) Commun. Nonlinear Sci. Numer. Simulat. , vol.15 , pp. 2003-2016
    • Liao, S.J.1
  • 21
    • 67349180749 scopus 로고    scopus 로고
    • Numerical solution of the generalized Zakharov equation by homotopy analysis method
    • Abbasbandy S., Babolian E., Ashtiani M. Numerical solution of the generalized Zakharov equation by homotopy analysis method. Commun. Nonlinear Sci. Numer. Simulat. 2009, 14:4114-4121.
    • (2009) Commun. Nonlinear Sci. Numer. Simulat. , vol.14 , pp. 4114-4121
    • Abbasbandy, S.1    Babolian, E.2    Ashtiani, M.3
  • 22
    • 77953992014 scopus 로고    scopus 로고
    • Analytic solution of the Sharma-Tasso-Olver equation by homotopy analysis method
    • Abbasbandy S., Ashtiani M., Babolian Esmail Analytic solution of the Sharma-Tasso-Olver equation by homotopy analysis method. Z. Naturforsch. 2010, 65a:285-290.
    • (2010) Z. Naturforsch. , vol.65 a , pp. 285-290
    • Abbasbandy, S.1    Ashtiani, M.2    Babolian, E.3
  • 23
    • 74149089078 scopus 로고    scopus 로고
    • Analytical approximate solutions of systems of fractional algebraic-differential equations by homotopy analysis method
    • Zurigat M., Momani S., Alawneh A. Analytical approximate solutions of systems of fractional algebraic-differential equations by homotopy analysis method. Comput. Math. Appl. 2010, 59:1227-1235.
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1227-1235
    • Zurigat, M.1    Momani, S.2    Alawneh, A.3
  • 24
    • 56549119386 scopus 로고    scopus 로고
    • The homotopy analysis method to solve the Burgers-Huxley equation
    • Molabahrami A., Khani F. The homotopy analysis method to solve the Burgers-Huxley equation. Nonlinear Anal.-Real 2009, 10:589-600.
    • (2009) Nonlinear Anal.-Real , vol.10 , pp. 589-600
    • Molabahrami, A.1    Khani, F.2
  • 25
    • 34249337378 scopus 로고    scopus 로고
    • The solution of coupled Burgers' equations using Adomian-Padé technique
    • Dehghan M., Hamidi A., Shakourifar M. The solution of coupled Burgers' equations using Adomian-Padé technique. Appl. Math. Comput. 2007, 189:1034-1047.
    • (2007) Appl. Math. Comput. , vol.189 , pp. 1034-1047
    • Dehghan, M.1    Hamidi, A.2    Shakourifar, M.3
  • 26
    • 33751538987 scopus 로고    scopus 로고
    • A new general algebraic method with symbolic computation and its application to two nonlinear differential equations with nonlinear terms of any order
    • Wang J., Zhang X.L., Song L.N., Zhang H.Q. A new general algebraic method with symbolic computation and its application to two nonlinear differential equations with nonlinear terms of any order. Appl. Math. Comput. 2006, 182:1330-1340.
    • (2006) Appl. Math. Comput. , vol.182 , pp. 1330-1340
    • Wang, J.1    Zhang, X.L.2    Song, L.N.3    Zhang, H.Q.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.