Application of Splines of the Second Order Approximation to Volterra Integral Equations of the Second Kind. Applications in Systems Theory and Dynamical Systems

Abstract

This paper discusses the application of local interpolation splines of the second order of approximation for the numerical solution of Volterra integral equations of the second kind. Computational schemes based on the use of polynomial and non-polynomial splines are constructed. The advantages of the proposed method include the ability to calculate the integrals which are present in the computational methods. The application of splines to the solution of nonlinear Volterra integral equations is also discussed. The results of numerical experiments are presented

On the numerical solution of Volterra integral equations on equispaced nodes

“…Several mathematical models arising in elasticity, scattering theory, seismology, heat conduction, fluid flow, chemical reactions, population dynamics, semi-conductors, and in other fields, involve Volterra equations of the type (1.1); see, e.g., [3,6,7,8,15,20,23,30].…”