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.


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