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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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