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Zbl 1180.65097
Huang, Chengming; Li, Wenhao
Delay-dependent stability analysis of the trapezium rule for a class of second order delay differential equations. (English)
[J] Chin. J. Numer. Math. Appl. 29, No. 3, 96-104 (2007); translation from Math. Numer. Sin. 29, No. 2, 155-162 (2007). ISSN 0899-4358

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.

MSC 2000:: *65L20 Stability of numerical methods for ODE
34K20 Stability theory of functional-differential equations
34K28 Numerical approximation of solutions of FDE
65L05 Initial value problems for ODE (numerical methods)

Keywords: boundary locus method; trapezium rule; delay-dependent stability; second-order delay differential equations

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