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On the order of convergence of Adomian method. (English) Zbl 1044.65043
The authors consider an approximate solution of the equation $$y-N(y)=f$$ where $$N$$ is a nonlinear operator from a Hilbert space onto itself. They state (without proof) that the Adomian decomposition method for the above equation is equivalent to solving the equation $$S=N(y_0+S)$$ by iteration, $$S_{n+1}=N(y_0+S_n)$$, and obtain the order of convergence of $$(S_n)$$ to $$S$$ under certain smoothness assumptions on $$N$$. Here $$y_0$$ is supposed to be $$f$$ and $$S=y-y_0$$.

##### MSC:
 65J15 Numerical solutions to equations with nonlinear operators 47J25 Iterative procedures involving nonlinear operators
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