A Taylor Series Method for the Solution of the Boundary Value Problems for Higher Order Ordinary Differential Equation

In this paper a numerical method for solving ordinary differential equation in boundary value condition is presented. In mathematics and other field by the use of Taylor series we solve the problems of linear and nonlinear ordinary differential equations and partial differential equations. Taylor series method is an important analytic-numeric method (algorithm) of ordinary differential equations for approximate solution of initial and boundary value problems due to calculation of higher order derivatives currently this algorithm is not applied frequently. Only explicit version is known in this algorithm. The main idea is based on the approximate calculation of higher derivatives. This paper describes several above-mentioned algorithms and examines its numerical solutions of ODE and It demonstrates some numerical test results for systems of equations The method is computationally attractive and application is demonstrated through illustrative examples.