Numerical Approximation of the Characteristic Values for a Delay Differential Equation 1999 2 citations ? 2 self

Abstract:  We present results on the approximation of the characteristic values of a delay differential equation through the calculation of characteristic values of a corresponding discrete scheme constructed through the use of a strongly stable linear multistep method. Our tool in the analysis is the boundary locus method and we give a theorem that guarantees that the roots of the characteristic equation of the delay equation are approximated by roots of the characteristic equation of the discrete scheme to the order of the method, as h ! 0. 1 Introduction Delay differential equations of the form y 0 (t) = f(y(t); y(t \Gamma 1 ); y(t \Gamma 2 ); : : : ; y(t \Gamma n )); y 2 R + ! R M ; 0 ! 1 ! 2 ! : : : ! n (1.1) have been considered by many authors (for example [2, 3, 4, 5, 11, 13, 12, 18]). Several recent papers ([7, 8, 9, 17]) have considered the stability or asymptotic stability of solutions to (1.1) and have also analysed, among stable solutions, the existence and natu...