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Approximate solutions to boundary value problems of higher order by the modified decomposition method. (English) Zbl 0959.65090
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.

MSC:
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
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References:
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