The numerical solution of differential equations with retarded argument by means of natural spline functions of even degree

Abstract

This paper presents a numerical method for the approximate solution of ordinary differential equations with retarded argument. This method is essentially based on the natural spline functions of even degree introduced by using the derivative-interpolating conditions on simple knots. The estimation of the error, as well as, the convergence of the proposed method are investigated. Some numerical examples are given.

Keywords:

• Natural spline function
• derivative-interpolating function
• initial value problem
• retarded argument differential equation

1980 Mathematics Subject Classification (1985 Revision):

• 41A15
• 65D07
• 65L05

C.R.Categories:

• G1.3
• G1.7