One relationship between Volterra integro-differential and ordinary differential equations

Abstract

There are some wide classes of the numerical methods to solving ODE. Therefore the specialists tried to apply these methods to solving of the Volterra integral and integro-differential equations. Here, we proposed the new relation between ODEs and Volterraintegro-differential equation, by using which have constructed the stable multistep methods, having the higher order of accuracy. Constructed the concrete methods, which are applied to solving model problem. And have shown that by using the same algorithm one can be solved the initial value problem for Volterraintegro-differential and ordinary differential equations.