On some comparison of the multistep hybrid methods and their application solving of the Volterra integro-differential equations

As is known, there are some classes of numerical methods for solving of the initial-value problem for the Volterra integro-differential equations. Here, by comparison of the known methods have constructed the methods with the new properties which have applied to solve the initial-value problem for the ODE and for the Volterra integra-differential equations. By the construction of some relation between of these equations have established the direct connection among them which have called as the p-equivalents between the initial-value problem for ODE and for the Volterra integro-differential equations. Constructed here the stable methods with the high order of accuracy show some advantages of them. Some of them are applied to solving of the initial-value problem for the Volterra integro-differential equations. And also for the illustration of the received results here constructed have applied one of these methods to solve the model problem.