A review of the decomposition method and some recent results for nonlinear equations. (English) Zbl 0713.65051

Adomian, G.

Math. Comput. Modelling 13, No. 7, 17-43 (1990).

An analytical method for approximate solution of nonlinear ordinary and partial differential equations (initial and boundary value problems) is briefly described and broadly illustrated on a considerable number of examples. In short, the method presupposes knowledge of the Green’s function of the highest derivative and starts from expanding the solution into a series \(u_ 0+\epsilon u_ 1+\epsilon^ 2u_ 2+...\), then expanding the nonlinearity into a Taylor series about \(u_ 0\) and putting then \(\epsilon =1\). A convergence proof for ordinary differential equations is announced.

Reviewer: G.Stoyan

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
65J99	Numerical analysis in abstract spaces
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

decomposition method; nonlinear equations; Green’s function; Taylor series; convergence

References:

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