Adomian, G. On the convergence region for decomposition solutions. (English) Zbl 0547.65053 J. Comput. Appl. Math. 11, 379-380 (1984). Summary: The author’s decomposition method using his \(A_ n\) polynomials for the nonlinearities has been shown to apply to wide classes of nonlinear (or nonlinear stochastic) operator equations providing a computable, accurate solution which converges rapidly. In computation the above is sufficient for a rapid test of convergence region. Cited in 14 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems Keywords:decomposition method; Newton’s methods; Picard methods; rapid test of convergence region × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Adomian, G., Stochastic Systems (1983), Academic Press: Academic Press New York · Zbl 0504.60066 [2] G. Adomian, Stochastic Systems II; G. Adomian, Stochastic Systems II · Zbl 0523.60056 [3] C. Adomian, Applications of Stochastic Systems Theory to Physics and Engineering; C. Adomian, Applications of Stochastic Systems Theory to Physics and Engineering · Zbl 0659.93003 [4] Adomian, G., Convergent series solution of nonlinear equations, J. Comput. Appl. Math., 12, 2, 225-230 (1984) · Zbl 0549.65034 [5] Bellman, R. E.; Adomian, G., Partial Differential Equation — New Methods for their Treatment and Application (1984), Reidel: Reidel Boston 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.