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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:

65L05 Numerical methods for initial value problems involving ordinary differential equations
44A10 Laplace transform
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A34 Nonlinear ordinary differential equations and systems

Citations:

Zbl 0802.65122

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