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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.

MSC:
47J05Equations involving nonlinear operators (general)
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References:
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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
[4] Cherruault, Y.; Saccomandi, G.; Somé, B.: New results for convergence of Adomian’s method applied to integral equations. Mathl. comput. Modelling 16, No. 2, 85-93 (1992) · Zbl 0756.65083
[5] Guellal, S.; Cherruault, Y.: Practical formulae for calculation of Adomian’s polynomials and application to the convergence of the decomposition method. Int. J. Of biomedical comp. 36, 223-228 (1994)
[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
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