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Zbl 0713.65051
Adomian, G.
A review of the decomposition method and some recent results for nonlinear equations.
(English)
[J] Math. Comput. Modelling 13, No.7, 17-43 (1990). ISSN 0895-7177

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 $u\sb 0+\epsilon u\sb 1+\epsilon\sp 2u\sb 2+...$, then expanding the nonlinearity into a Taylor series about $u\sb 0$ and putting then $\epsilon =1$. A convergence proof for ordinary differential equations is announced.
[G.Stoyan]
MSC 2000:
*65L10 Boundary value problems for ODE (numerical methods)
65J99 Numerical analysis in abstract spaces
34B15 Nonlinear boundary value problems of ODE

Keywords: decomposition method; nonlinear equations; Green's function; Taylor series; convergence

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