Numerical oscillations analysis for nonlinear delay differential equations in physiological control systems (Q1952827)

Summary: This paper deals with the oscillations of numerical solutions for nonlinear delay differential equations in physiological control systems. The exponential \(\theta\)-method is applied to \[ p'(t) = \beta_0 \omega^\mu p(t - \tau)/(\omega^\mu + p^\mu(t - \tau)) - \gamma p(t), \] and it is shown that the exponential \(\theta\)-method has the same order of convergence as that of the classical \(\theta\)-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every non-oscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.