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New ideas for proving convergence of decomposition methods. (English) Zbl 0832.47051
Summary: We give new formulae which calculate easily the Adomian’s polynomials used in decomposition methods. Then, the proof of convergence of the Adomian’s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation.

47J05Equations involving nonlinear operators (general)
Full Text: DOI
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[2] K. Abbaoui and Y. Cherruault, Convergence of Adomian’s method applied to differential equations, Mathl. Comput. Modelling28 (5), 103--110. · Zbl 0809.65073
[3] Cherruault, Y.: Convergence of Adomian’s method. Kybernetes 18, No. 2, 31-38 (1989) · Zbl 0697.65051
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[6] Adomian, G.: A review of decomposition method and some recent results for nonlinear equations. Mathl. comput. Modelling 13, No. 7, 17-43 (1990) · Zbl 0713.65051
[7] Chandrasekharan, K.: Arithmetical functions. (1970) · Zbl 0217.31602
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