A way for finding the relation between of the degree and order for multistep method used to applied to solving of the Volterra integro-differential equation

摘要

As is known there are some classes of numerical methods have constructed to solving initial value problem of the ODE, which fundamentally investigated by the many known scientist. Therefore the specialists tried to study many scientific and applied problems by using these methods. Here we have defined the direct way between the initial value problem for the Volterra integro-differential and Ordinary Differential Equations. By using this way have constructed the multistep methods with constant coefficients, which are applied to solving initial value problem for the Volterra integro-differential equations and have determined the necessary and sufficient conditions for its convergence. And also have proven that the constructed here methods are more accurately than the known, which is illustrated by the application of concrete method to solving of the model problem.