ON SOME COMPARISON THE METHODS OF RUNGE-KUTTA AND MULTI-STEP TYPES.

There are exactly two popular classes of methods to solve the initial-value problem for Ordinary Differential Equations, which are usually called the Runge-Kutta and Multistep methods. Each method of these classes has its advantages and disadvantages. Note that at the intersection of these methods, there is one method the explicit Euler method. The main difference between this class of methods is that in the class of Multistep methods, there are implicit methods. However, this cannot be said about the classic Runge-Kutta method. Here have investigated these class methods, considering to construction of stable methods with a high degree. And also recommended to construct a method that preserves some properties of the Runge-Kutta methods and also some properties of the Multistep Methods with constant coefficients. By using the Runge-Kutta methods are one-step, here by changing the values of step size, recommended to construct methods at the intersection of these methods. It is also shown that depending on the nature of solving problems, these methods can coincide.