Delay-dependent stability analysis of trapezium rule for second order delay differential equations with three parameters

This paper is concerned with the study of the stability properties of trapezium rule for second order delay differential equations with three parameters. We start with introducing the analytical stability of a model equation. Then by using the boundary locus method, the delay-dependent stability region of the trapezium rule is analyzed and its boundary is found. Finally, a comparison between analytical and numerical stability regions is made and it is proved that the trapezium rule can completely preserve the delay-dependent stability of the underlining equations.