Oscillation Analysis Of Two Kinds Of Systems With Piecewise Continuous Arguments

This paper mainly uses the ?-methods to analyze the oscillation of two kind-s of systems with piecewise continuous arguments.At present,the research on the oscillation of systems with piecewise continuous arguments is more and more comprehensive.However,the discussion of numerical oscillation is very limited.In recent years,the treatment methods of numerical oscillation mainly include linear ?-methods,linear multistep methods and Runge-Kutta methods.So far,the research on numerical oscillation is limited to 1 dimensional case.This paper extends the relevant conclusions to 2 dimensional case to better analyze and deal with practical problems.In this paper,the background and significance of delay differential equations are described,and the research status of oscillation is given.Then,the basic definitions and important theorems of oscillation solutions for delay differential equations and difference equations are discussed.After that,the ?-method is used to analyze the oscillation and non-oscillation of analytic solution and numerical solution for a kind of differential equations with piecewise continuous arguments of retarded type,and the sufficient conditions for the numerical methods to preserve the oscillation of the equation under the condition of the analytic solution oscillation are obtained At the same time,some numerical experiments are given.At last,the oscillation of analytic solution of a kind of systems with piecewise continuous arguments of advanced type is studied.The oscillation of the numerical solution is obtained by using the ?-method,and the preservation of oscillation is discussed.Meanwhile,some numerical experiments are given.