Periodic solutions to functional evolution equations
The authors first discuss stability properties of delay differential equations (DDEs). Then they compare and extend this analysis to linear multistep methods methods applied to DDEs. The characteristic roots of the system of DDEs are important in the context of stability and bifurcation analysis. They prove convergence orders for the charaeristic root approximations and analyze under what condition for the steplength the discrete integration scheme retains certain delay-independent stablility properties of the original equations. The authors concentrate on the recovery of both stability and instability. These findings are illustrated with a number of numerical test results.
scientific article; zbMATH DE number 1880098