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Delay-dependent stability analysis of the trapezium rule for a class of second order delay differential equations. (English) Zbl 1180.65097
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:
65L20Stability and convergence of numerical methods for ODE
34K20Stability theory of functional-differential equations
34K28Numerical approximation of solutions of functional-differential equations
65L05Initial value problems for ODE (numerical methods)