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Decomposition methods: A new proof of convergence. (English) Zbl 0805.65057
The authors consider nonlinear equations of the form (*) $u-N(u)=f$ where $N$ and $f$, respectively, are operator and function given in convenient spaces. They construct a solution of (*) in the form (+) $u=\sum\sp \infty\sb{i=0} u\sb i$ where the $u\sb i$ are successively defined. A convergence proof of the series (+) is proposed and the error of the truncated series of (+) is estimated. No application is given. [Remark: The proof is not very distinct; in particular, the space in which the proof is valid is not stated].

65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
Full Text: DOI
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[7] L. Gabet, Modélisation de la diffusion des médicaments à travers les capillaires et dans les tissus à la suite d’une injection et Esquisse d’une thérorie décompositionnelle et applications aux équations aux dérivées partielles, Thèse de l’Ecole Centrale de Paris, (July 1, 1992)
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