The aim of this book is to present a method for solution of system of first order initial value problems of ordinary differential equation by a semi -analytic technique with constructing polynomial solutions . The original problem is concerned using two -point o sculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] and give some examples illustrate suggested method and accuracy, easily implemented. The accuracy of the method is confirmed by compared with conventional methods ( RK4, RK -Butcher , DTM , HPM , ABM ...