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Zbl 0996.65068
Khuri, Suheil A.
A Laplace decomposition algorithm applied to a class of nonlinear differential equations. (English)
[J] J. Appl. Math. 1, No.4, 141-155 (2001). ISSN 1110-757X; ISSN 1687-0042/e

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 {\it 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.
[Manfred Tasche (Rostock)]

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
44A10 Laplace transform
34A25 Analytical theory of ODE
34A34 Nonlinear ODE and systems, general

Keywords: decomposition method; Laplace transform; initial value problem; nonlinear differential equation; Adomian polynomials; numerical examples

Citations: Zbl 0802.65122

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