Piecewise Continuous Differential Equations Stability Of The Euler-maclaurin Method

This paper mainly deals with the convergence and the numerical stability ofdelay diferential equations with piecewise continuous arguments. This kind of equa-tions has considerable applications to physics, biology systems and control theory.Therefore, the stability analysis of the numerical solutions is of important theoreticaland practical signifcance.The convergence and stability of the Euler-Maclaurin method for the advanceddelay diferential equations with piecewise continuous arguments are investigated.It is proved that the nth-Euler-Maclaurin method is of2n+2order. The conditionsthat the stability region of the numerical solutions contains the stability region ofthe analytic solutions are obtained.The convergence and stability of the numerical solutions for the unbounded re-tarded delay diferential equations with piecewise continuous arguments is discussedin this paper. It is proved that the nth-Euler-Maclaurin method is of2n+2order,and for all Euler-Maclaurin method, the stability region of the numerical methodcontains the stability region of the analytic solutions.Moreover, the relevant numerical examples are given in every part. These ex-periments verify the results obtained in the theoretical analysis.