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This paper focuses on the stability and oscillations of Euler-Maclaurin method for linear differential equations with piecewise constant arguments u′ (t) = αu(t) + bu([t]). The necessary and sufficient conditions under which the numerical stability region contains the analytical stability region are given. Furthermore, the conditions of oscillation for the Euler-Maclaurin method are obtained. We prove that the Euler-Maclaurin method preserves the oscillations of the analytic solution. Moreover, the relationships between stability and oscillations are discussed for analytic solution and numerical solution, respectively. Finally, some numerical experiments for verifying the theoretical analysis are also provided. [ABSTRACT FROM AUTHOR]

We consider the oscillations of numerical solutions for the nonlinear delay differential equations in the control of erythropoiesis. The exponential ϑ-method is constructed and some conditions under which the numerical solutions oscillate are presented. Moreover, it is proven that every nonoscillatory numerical solution tends to the equilibrium point of the continuous system. Numerical examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential ?-method is applied to p(t)D ß0?µp(t-t)/(?µ)(pµ(t-t))-?p(t) and it is shown that the exponential ?-method has the same order of convergence as that of the classical ?-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustratedwith numerical examples. [ABSTRACT FROM AUTHOR]