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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 θ-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.
MSC:
65L03Functional-differential equations (numerical methods)
92D25Population dynamics (general)
92C50Medical applications of mathematical biology
34K11Oscillation theory of functional-differential equations
34K28Numerical approximation of solutions of functional-differential equations
65L20Stability and convergence of numerical methods for ODE
65L12Finite difference methods for ODE (numerical methods)