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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:
65L05Initial value problems for ODE (numerical methods)
34L30Nonlinear ordinary differential operators
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
65L70Error bounds (numerical methods for ODE)
WorldCat.org
Full Text: DOI
References:
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