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Derivation of the Adomian decomposition method using the homotopy analysis method. (English) Zbl 1125.65063
The solution of a nonlinear equation $L(y(x)) + N(y(x)) = 0$, where $L$ and $N$ are linear and nonlinear operators, respectively, is represented in the form $$y =\sum_{n=0}^{\infty} y_{n} .$$ The terms $y_{n}$ can be calculated by recurrent relations using the decomposition $$N(y)=\sum_{n=0}^{\infty} A_{n},$$ where $A_{n}$ are the Adomian polynomials. The author proves that this method can be obtained using another analytical method.

##### MSC:
 65L05 Initial value problems for ODE (numerical methods) 34L30 Nonlinear ordinary differential operators 34A25 Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.) 65L70 Error bounds (numerical methods for ODE)
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