Approximate solutions to boundary value problems of higher order by the modified decomposition method (Q1591925)

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.