Oscillation Analysis Of Numerical Solutions For Two Kinds Of Delay Differential Equations

This paper mainly deals with the oscillation of numerical solutions of two kinds of equations with piecewise continuous arguments,which are widely used in real life,such as neural networks in biology;hematopoiesis in population dynamics;automat-ic control systems in engineering etc.The solution of the equations is continuous at the ends connecting any two adjacent intervals and the solution has some recurrence relation at these ends.So the equation has the characteristics of differential equa-tion and difference equation.At present,?-methods and Runge-Kutta methods are the main methods to study the oscillation of the numerical solution of the equations with piecewise continuous arguments,while the other numerical methods are rare In this paper,the Euler-Maclaurin method and exponential ?-methods are mainly considered to study the condition for the oscillation of numerical solutions of several kinds of equations and the conditions for the numerical methods to maintain the oscillation of analytical solutionsIn the third chapter,we study the numerical oscillation of the Euler-Maclaurin method for solving the equations with EPCA.By discussing the equivalence of oscillation for numerical solutions on the integer nodes and any nodes.The sufficient and necessary conditions for the oscillation of the numerical solution with a? 0 and a?0.The conditions for the numerical method to preserve the oscillation and nonoscillation of the analytical solution are obtained.At last,the corresponding numerical examples are givenIn the fourth chapter,the numerical oscillation of the exponential 0-methods for solving the equations with EPCA is studied.In this chapter,the numerical oscillation of the equation with constant coefficient and the numerical nonoscilla-tion of the equation with matrix coefficient are analyzed.For the equation with constant coefficients,the necessary and sufficient conditions oscillation for numer-ical solutions of equations with piecewise continuous arguments are obtained.For the equation with matrix coefficients,the necessary and sufficient conditions for the nonoscillation are obtained.At the same time,the conditions are that the numerical methods preserve the nonoscillation of the analytical solution of the equation is also considered.At last,the corresponding numerical examples are given.