Convergence of Adomian's method applied to nonlinear equations
The nonlinear equation \(f(x)= 0\) in \(\mathbb{R}\) is transformed into the form \(x= F(x)+ c\) (\(F\) is a nonlinear function, \(c\) is constant). The solution of the latter is calculated in the series form \(x= \sum^ \infty_{i= 0} x_ i\) and \(F(x)= \sum^ \infty_{i= 0} A_ i\), where \(A_ i\)'s are Adomian polynomials. The authors derive the convergence conditions and give the numerical examples.
scientific article; zbMATH DE number 722506