zbMATH — the first resource for mathematics

Delay-dependent stability analysis of the trapezium rule for a class of second order delay differential equations. (English) Zbl 1180.65097
Chin. J. Numer. Math. Appl. 29, No. 3, 96-104 (2007); translation from Math. Numer. Sin. 29, No. 2, 155-162 (2007).
Summary: This paper is concerned with the study of the stability of numerical methods for a class of second-order delay differential equations. By using the boundary locus method, the delay-dependent stability region of the trapezium rule is analyzed and its boundary is found. Then the relationship between analytical and numerical stability regions is identified and it is proved theoretically that the trapezium rule can completely preserve the delay-dependent stability for the considered set of test problems.

65L20 Stability and convergence of numerical methods for ordinary differential equations
34K20 Stability theory of functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
65L05 Numerical methods for initial value problems involving ordinary differential equations