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Convergence of Adomian’s method applied to differential equations. (English) Zbl 0809.65073

The authors present a new proof of the convergence of Adomian’s method applied to differential equations. They give some new formulae and properties and suggest a simple computational form for Adomian’s polynomials.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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References:

[1] Adomian, G., Nonlinear Stochastic Systems Theory and Applications to Physics (1989), Kluwer · Zbl 0659.93003
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[9] Schwartz, L., Cours d’Analyse (1981), Hermann: Hermann Paris
[10] Rach, R., A convenient computational form of the Adomian’s plynomials, J. Math. Anal. App., 102, 45-419 (1984) · Zbl 0552.60061
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