Jafari, Hossein; Daftardar-Gejji, Varsha Revised Adomian decomposition method for solving a system of nonlinear equations. (English) Zbl 1088.65047 Appl. Math. Comput. 175, No. 1, 1-7 (2006). Summary: A modification of Adomian decomposition method is suggested and used for solving a system of nonlinear equations, which yields a series solution with accelerated convergence. Illustrative examples are presented to demonstrate the method, and the results obtained are compared with those derived from the standard Adomian decomposition method. Cited in 1 ReviewCited in 32 Documents MSC: 65H10 Numerical computation of solutions to systems of equations Keywords:Adomian polynomials; Convergence acceleration; Numerical examples; Comparison of methods PDF BibTeX XML Cite \textit{H. Jafari} and \textit{V. Daftardar-Gejji}, Appl. Math. Comput. 175, No. 1, 1--7 (2006; Zbl 1088.65047) Full Text: DOI References: [1] Abboui, K.; Cherruault, Y.; Seng, V., Practical formula for the calculus of multivariable Adomian polynomials, Math. Comput. Modell., 22, 1, 89-93 (1995) · Zbl 0830.65010 [2] Abboui, K.; Cherruault, Y., Convergence of Adomian’s method applied to non-linear equations, Math. Comput. Modell., 20, 9, 69-73 (1994) · Zbl 0822.65027 [3] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer · Zbl 0802.65122 [4] Adomian, G., A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135, 501-544 (1988) · Zbl 0671.34053 [5] Babolian, E.; Biazar, J.; Vahidi, A. R., Solution of a system of nonlinear equations by Adomian decomposition method, J. Math. Anal. Appl., 150, 3, 847-854 (2004) · Zbl 1075.65073 [6] Babolian, E.; Biazar, J., Solution of a system of nonlinear Volterra integral equations of the second kind, Far East J. Math. Sci., 2, 6, 935-945 (2000) · Zbl 0979.65123 [7] Biazar, J.; Babolian, E.; Islam, R., Solution of the system of ordinary differential equations by Adomian decomposition method, Appl. Math. Comput., 147, 3, 713-719 (2004) · Zbl 1034.65053 [8] 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 [9] Daftardar-Gejji, V.; Jafari, H., Adomian decomposition: a tool for solving a system of fractional differential equations, J. Math. Anal. Appl., 301, 2, 508-518 (2005) · Zbl 1061.34003 [11] Kaya, D.; El-Sayed, S. M., A numerical solution of the Klein-Gordon equation and convergence of the decomposition method, Appl. Math. Comput., 156, 2, 341-353 (2004) · Zbl 1084.65101 [12] Shawagfeh, N. T., Analytical approximate solutions for nonlinear fractional differential equations, Appl. Math. Comput., 131, 517-529 (2002) · Zbl 1029.34003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.