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 (+) \(u=\sum^ \infty_{i=0} u_ i\) where the \(u_ i\) 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].


65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
Full Text: DOI


[1] Cherruault, Y., Convergence of Adomian’s method, Kybernetes, 18, 2, 31-38 (1989) · Zbl 0697.65051
[2] Cherruault, Y.; Saccomandi, G.; Somé, B., New results for convergence of Adomian’s method applied to integral equations, Math. Comput. Modelling, 16, 2, 85-93 (1992) · Zbl 0756.65083
[3] Adomian, G., Nonlinear Stochastic Systems Theory and Applications to Physics (1989), Kluwer · Zbl 0659.93003
[4] Adomian, G., Solving frontier problems of physics: The decomposition method (1993), (to appear) · Zbl 0814.47070
[5] Adomian, G.; Rach, R. C.; Meyers, R. E., An efficient methodolgy for the physical sciences, Kybernetes, 20, 7, 24-34 (1991) · Zbl 0744.65039
[6] Adomian, G., An analytical solution of the stochastic Navier-Stokes problem, Foundations of Physics, 21, 7, 831-843 (1991)
[9] Cherruault, Y., New deterministic methods for global optimization and application to biomedicine, Int. J. Biomed. Comput., 27, 215-229 (1991)
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.