Integral equations and their relationship to differential equations with initial conditions

Abstract EN

Integral and differential equations have a fundamental importance in the functional analysis and the practice problems, and many domains of scientific research.

However, the resolution of differential equations with constant coefficients is easy, but the resolution of these equations with variable coefficients is practically difficult or impossible in more part of the cases.

This work present a analytical method which it transform a differential equations with initial conditions to a Volterra equations of second kind, efficient methods for approximate numerical solution of these equations, the analysis of the existence of their solutions, and the convergence of the error.