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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 Numerical methods for initial value problems involving ordinary differential equations 34L30 Nonlinear ordinary differential operators 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 65L70 Error bounds for numerical methods for ordinary differential equations
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