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Zbl 1237.65064
Gao, Jianfang; Song, Minghui; Liu, Mingzhu
Oscillation analysis of numerical solutions for nonlinear delay differential equations of population dynamics.
(English)
[J] Math. Model. Anal. 16, No. 3, 365-375 (2011). ISSN 1392-6292; ISSN 1648-3510/e

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.
[Rémi Vaillancourt (Ottawa)]
MSC 2000:
*65L03
92D25 Population dynamics
92C50 Medical appl. of mathematical biology
34K11 Oscillation theory of functional-differential equations
34K28 Numerical approximation of solutions of FDE
65L20 Stability of numerical methods for ODE
65L12 Finite difference methods for ODE

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

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