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New results for convergence of Adomian’s method applied to integral equations. (English) Zbl 0756.65083
Consider the general functional equation (1) $y-N(y)=f$, where $N$ is a nonlinear operator from a Hilbert space $H$ into itself and $f$ is a given element in $H$. The paper presents a new convergence proof of Adomian’s method which consists in solving (1) by means of representing $y$ as an infinite series. Some applications of this technique to nonlinear integral equations are given.

65J15Equations with nonlinear operators (numerical methods)
65R20Integral equations (numerical methods)
45G10Nonsingular nonlinear integral equations
47J25Iterative procedures (nonlinear operator equations)
Full Text: DOI
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