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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.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
47J25 Iterative procedures involving nonlinear operators
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References:

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