Oscillation analysis of numerical solutions for nonlinear delay differential equations of population dynamics. (English) Zbl 1237.65064

The authors investigate oscillations of the numerical solution of a nonlinear delay differential equation of population dynamics. An exponential convergence linear \(\theta\)-method is constructed. They obtain conditions under which the numerical solution oscillates in the case of oscillations of the analytic solution. It is proved that non-oscillatory numerical solutions can preserve properties of non-oscillatory analytic solutions. Applications are to a “dynamic disease” which involves respiratory disorders, called Cheyne-Stokes respiration.


65L03 Numerical methods for functional-differential equations
92D25 Population dynamics (general)
92C50 Medical applications (general)
34K11 Oscillation theory of functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
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