A Laplace decomposition algorithm applied to a class of nonlinear differential equations (Q1598936)

Using Laplace transform, the author constructs recursively an approximate solution of an initial value problem of the nonlinear differential equation \[ y''+ a(x)y'+ b(x) y= f(y), \] where the nonlinear term \(f(y)\) is decomposed in terms of Adomian polynomials [see \textit{G. Adomian}, Solving frontier problems of physics: The decomposition method, Kluwer, Dordrecht (1994; Zbl 0802.65122)]. But the convergence of this method is not considered. Some numerical examples are given, where higher iterates of the approximate solution are computed by a computer algebra system.