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On an application of hybrid method to the solution of Volterra nonlinear integro-differential equation

While constructing mathematical model of some phenomena of nature we meet the solution of initial value problem for Volterra integro-differential equation. Many papers have been devoted to the numerical solution of this problem. In these works, at first the integral is replaced by the integral sum then one of the well investigated numerical methods from the class of numerical methods for solving ordinary differential equations is applied to the obtained one. Notice that in the methods suggested in these papers, mainly a variable boundary integral sum assisting to increase the volume of calculations while parsing from one point to another one is used. Therefore, we try to construct a method that preserves constant amount of calculations at each point.