## 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:

 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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### References:

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