Stability of Backward Differential Formulae for Second Order Delay Differential Equations

Abstract

This paper is concerned with the numerical stability of backward differential formulae for the second order differential equations with a lagging argument. A sufficient condition such that this kind of system is asymptotically stable is derived. Furthermore, it is proved that every A-stable BDF method preserves the stable properties of exact solutions for the second order delay differential equations. Finally, some numerical experiments are given to demonstrate the main conclusions. © Springer-Verlag Berlin Heidelberg 2006.