A continuous implicit nyström method for solving ordinary second order initial value problems

Abstract

This paper is concerned with the construction of a new formula for integrating special second order, periodic and nonperiodic, initial value problems in ordinary differential equations. The presented formula is based on C ²-cubic splines as an approximation to the exact solution of the initial value problem,

It turns out that the proposed method is a continuous extension of the well-known second order 1-stage implicit Nyström method and hence possesses nonvanishing intervals of periodicity and absolute stability.

Keywords:

• Second order initial value problems
• Nyström method
• collocation methods
• absolute stability
• periodic stability

AMS Subject classification:

• 65L06

C.R. Categories:

• G.1.7