On the use of spline functions of even degree for the numerical solution of the delay differential equations

Abstract

One considers and investigates the notion of natural spline functions of even degree, satisfying given derivative-interpolating conditions on simple knots. By using such spline functions we shall develop some theory and algorithms for the numerical solution of a class of delay differential equations. It will be shown that such kind of spline functions are very suitable for the numerical treatment of delay differential equations with initial conditions.