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

Gao, Jianfang; Song, Minghui; Liu, Mingzhu

Math. Model. Anal. 16, No. 3, 365-375 (2011).

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.

Reviewer: Rémi Vaillancourt (Ottawa)

MSC:

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

Keywords:

oscillation; nonlinear delay differential equation; population dynamics; exponential convergence; linear \(\theta\)-method; dynamic disease; Cheyne-Stokes respiration