Semi-Analytic Method for Solving High Order Ordinary Differential Equations with Initial Condition

Abstract

The aim of this paper is to present method for solution high order ordinary differential equations with initial condition using semi-analytic technique with constructing polynomial solutions. The original problem is concerned using two-point 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 (Runga-Kutta (RK4), RK-Butcher ,Differential Transformation method (DTM) ) . The sensitivity of solutions high order ordinary differential equations with initial condition is discussed .