Some investigation of the numerical solution of ordinary differential equations

With the numerical solution of ordinary differential equations(ODE), scientists engaged in the Middle Ages, beginning with the work of Clairaut. The domain of the numerical methods involved in many famous mathematicians - Euler, Runge, Kutta, Adams, Laplace, and others. They have constructed methods with different properties. In this paper we consider the construction of numerical methods with high accuracy and to this end is proposed to use multistep multiderivative and hybrid methods. As well as specific methods are constructed with a certain accuracy.