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