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

Khuri, Suheil A.

J. Appl. Math. 1, No. 4, 141-155 (2001).

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.

Reviewer: Manfred Tasche (Rostock)

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

Keywords:

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

Citations:

Zbl 0802.65122

Software:

Maple