Euler-maclaurin Method Delay Differential Equations With Piecewise Continuous Oscillation Remain Independent Variable

As important mathematics models, delay diferential equations with piecewisecontinuous arguments (EPCA) have a wide range of applications in physics, biologyand control theory. Now there have been a lot of literatures concerning propertiesof EPCA, and a lot of important conclusions have been given. At the same time,there has been much research activity concerning the numerical methods of EPCA.The paper deals with preservation of oscillations of the Euler-Maclaurin method forEPCA.In the first chapter, we introduce the process of research and development ofdelay diferential equations,and points out the equations's applications in practicalproblem. Review of the research process for analytic solutions of delay diferentialsequations, as well as the numerical methods for delay diferential equations. Oscil-lation is an important aspect of the study of delay diferential equations. Therefore,research of delay diferential equation is an important research topic.In the second chapter,aiming at retarded EPCA, we first study the oscillationsof the analytic solution of the equation, then to deal with the equation with Euler-Maclaurin method, finally discuss the condition for preservation of oscillation ofnumerical solution.In the third chapter,aiming at advanced EPCA,we first study the oscillationsof the analytic solution of the equation, then to deal with the equation with Euler-Maclaurin method, finally discuss the condition for preservation of oscillation ofnumerical solution.