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An iterative method for solving nonlinear functional equations. (English) Zbl 1087.65055
Summary: An iterative method for solving nonlinear functional equations, viz. nonlinear Volterra integral equations, algebraic equations and systems of ordinary differential equation, nonlinear algebraic equations and fractional differential equations is discussed.

65J15Equations with nonlinear operators (numerical methods)
45G10Nonsingular nonlinear integral equations
65R20Integral equations (numerical methods)
65H10Systems of nonlinear equations (numerical methods)
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
Full Text: DOI
[1] Adomian, G.: Solving frontier problems of physics: the decomposition method. (1994) · Zbl 0802.65122
[2] Babolian, E.; Biazar, J.; Vahidi, A. R.: Solution of a system of nonlinear equations by Adomian decomposition method. J. math. Anal. appl. 150, 847-854 (2004) · Zbl 1075.65073
[3] 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
[4] Biazar, J.; Babolian, E.; Islam, R.: Solution of the system of Volterra integral equations of the first kind by Adomian decomposition method. Appl. math. Comput. 139, 249-258 (2003) · Zbl 1027.65180
[5] Cherruault, Y.: Convergence of Adomian’s method. Kybernetes 8, 31-38 (1988) · Zbl 0697.65051
[6] Daftardar-Gejji, V.; Jafari, H.: Adomian decomposition: a tool for solving a system of fractional differential equations. J. math. Anal. appl. 301, 508-518 (2005) · Zbl 1061.34003
[7] El-Sayed, S. M.: The modified decomposition method for solving nonlinear algebraic equations. Appl. math. Comput. 132, 589-597 (2002) · Zbl 1031.65067
[8] H. Jafari, V. Daftardar-Gejji, Revised Adomian decomposition method for solving a system of nonlinear equations, submitted for publication · Zbl 1088.65047
[9] H. Jafari, V. Daftardar-Gejji, Solving system of nonlinear fractional differential equations, submitted for publication · Zbl 1099.65137
[10] Jerri, A. J.: Introduction to integral equations with applications. (1999) · Zbl 0938.45001
[11] Ouedraogo, R. Z.; Cherruault, Y.; Abbaoui, K.: Convergence of Adomian’s decomposition method applied to algebraic equations. Kybernetes 29, 1298-1305 (2000) · Zbl 0994.65054
[12] Podlubny, I.: Fractional differential equations. (1999) · Zbl 0924.34008
[13] Wazwaz, A.: A first course in integral equations. (1997) · Zbl 0924.45001
[14] Wazwaz, A.: A reliable modification of Adomian decomposition method. Appl. math. Comput. 102, 77-86 (1999) · Zbl 0928.65083