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Zbl 0959.65090
Wazwaz, A.-M.
Approximate solutions to boundary value problems of higher order by the modified decomposition method.
(English)
[J] Comput. Math. Appl. 40, No.6-7, 679-691 (2000). ISSN 0898-1221

The author studies boundary value problems such as the following $$f^{(2m)}(x)= f(x,y),\quad 0\prec x\prec 1$$ with boundary conditions $$y^{(2j)}(0)= \alpha_{2j},\quad y^{(2j)}(1)= \beta_{2j},\quad j= 0,1,\dots,(m- 1).$$ The solution is found by using the decomposition method of Adomian searching $y(x)$ as a series $\sum^\infty_{n=0} y_n(x)$ and decomposing the nonlinear function by an infinite series of (Adomian) polynomials: $$f(x, y)= \sum^\infty_{n=0} A_n.$$ Numerical examples are treated and they prove the high accuracy of the Adomian method.
[Yves Cherruault (Paris)]
MSC 2000:
*65L10 Boundary value problems for ODE (numerical methods)
34B15 Nonlinear boundary value problems of ODE

Keywords: Adomian decomposition method; numerical examples; boundary value problems

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