Babolian, E.; Biazar, J. Solution of nonlinear equations by modified Adomian decomposition method. (English) Zbl 1023.65040 Appl. Math. Comput. 132, No. 1, 167-172 (2002). Summary: We modify the standard Adomian method for solution of a nonlinear equation \(f(x)=0\). Four examples are presented and compared using standard and modified Adomian methods. Cited in 2 ReviewsCited in 47 Documents MSC: 65H05 Numerical computation of solutions to single equations Keywords:numerical examples; Adomian method; nonlinear equation PDFBibTeX XMLCite \textit{E. Babolian} and \textit{J. Biazar}, Appl. Math. Comput. 132, No. 1, 167--172 (2002; Zbl 1023.65040) Full Text: DOI References: [1] Adomian, G., Nonlinear Stochastic Systems and Applications to Physics (1989), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0698.35099 [2] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0802.65122 [3] Adomian, G.; Rach, R., On the solution of algebraic equations by the decomposition method, Math. Anal. Appl., 105, 1, 141-166 (1985) · Zbl 0552.60060 [4] Adomian, G.; Saarafyan, D., Numerical solution of differential equations in the deterministic limit of stochastic theory, Appl. Math. Comput., 8, 111-119 (1981) · Zbl 0466.65046 [5] Adomian, G.; Rach, R., Non-linear stochastic differential delay equations, J. Math. Anal. Appl., 91, 1 (1983) · Zbl 0504.60067 [6] Bellman, R.; Adomian, G., Partial Differential Equations (1985), Reidel: Reidel Dordrecht [7] Adomian, G., Convergent series solution of non-linear equations, J. Comput. Appl. Math., 11, 225-230 (1984) · Zbl 0549.65034 [8] Cherruault, Y., Convergence of Adomian’s method, Kybernetes, 9, 2, 31-38 (1988) · Zbl 0697.65051 [9] Cherruault, Y.; Adomian, G., Decomposition method: a new proof of convergence, Math. Comput. Modelling, 18, 12, 103-106 (1993) · Zbl 0805.65057 [10] Abbaoui, K.; Cherruault, Y., Convergence of Adomian’s method applied to differential equatons, Math. Comput. Modelling, 28, 5, 103-110 (1994) · Zbl 0809.65073 [11] Cherruault, Y.; Saccamondi, G.; Some, B., New results of convergence of Adomian’s Method applied to integral equations, Math. Comput. Modelling, 16, 2, 85-93 (1992) · Zbl 0756.65083 [12] Abbaoui, K.; Cherruault, Y., Convergence of adomian’s method applied to non-linear equations, Comput. Math. Appl., 28, 5, 103-109 (1994) · Zbl 0809.65073 [13] Babolian, E.; Biazar, J., On the order of convergence of Adomian Method, Appl. Math. Comput., 130, 383-387 (2002) · Zbl 1044.65043 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.