The aim of this paper is to present method for solving high order nonlinear ordinary
differential equations with initial conditions using semi-analytic technique with
constructing polynomial solutions. The original problem is concerned using twopoint
osculatory interpolation with the fit equal numbers of derivatives at the end
points of an interval [0, 1] and give example illustrate suggested method and
accuracy, easily implemented. The accuracy of the method is confirmed by
compared with conventional methods ( RK4, RK-Butcher, DTM ).
The existence, uniqueness and sensitivity of the solution is discussed.