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A Laplace decomposition algorithm applied to a class of nonlinear differential equations. (English) Zbl 0996.65068

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 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.

MSC:
65L05Initial value problems for ODE (numerical methods)
44A10Laplace transform
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
34A34Nonlinear ODE and systems, general