Stability Analysis Of One-leg Methods For Nonlinear Functional Differential And Functional Equations With Two Delays

Functional diferential and functional equations(FDFEs) are a class of hybridproblem formed by functional diferential equations and functional equations.The class of hybrid problem arises widely in the felds of science and engineering.It is meaningful to investigate the theory and application of numerical methods forFDFEs. For the class of hybrid problem, the stability of numerical methods hasbeen discussed by several authors, where the problem only has a constant delay.However, the problem with multiple delays has been found in many practicalfelds, which means that the right function of the problem depends on the stateof the system in the past several times. The research of FDFEs with multipledelays is more complex. Up to now, we haven’t seen the literature with respectto this problem. In view of this, the present paper investigates the stability ofone-leg methods for a class of nonlinear FDFEs with two delays. The stabilityand asymptotic stability conditions of the methods are derived. Numerical testshave given to confrm the theoretical results in the end.