Delay-dependent stability of symmetric boundary value methods for second order delay differential equations with three parameters

This paper aims at the delay‐dependent stability analysis of symmetric boundary value methods, which include the Extended Trapezoidal Rules of the first kind and the second kind, the Top Order Methods and the B‐spline linear multistep methods, for second order delay differential equations with three parameters. Theoretical analysis and numerical results are presented to show that the symmetric boundary value methods preserve the asymptotic stability of the true solutions of the test equation.