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Zbl 1125.65063
Allan, Fathi M.
Derivation of the Adomian decomposition method using the homotopy analysis method. (English)
[J] Appl. Math. Comput. 190, No. 1, 6-14 (2007). ISSN 0096-3003

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.
[Ivan Secrieru (Chişinău)]

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34L30 Nonlinear ordinary differential operators
34A25 Analytical theory of ODE
65L70 Error bounds (numerical methods for ODE)

Keywords: nonlinear differential equation; analytical solution; method of decomposition in series; error analysis; convergence criteria

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Zentralblatt MATH Berlin [Germany]