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The discrete dynamics of nonlinear infinite-delay-differential equations. (English) Zbl 1001.65091

Nonlinear stability criteria are established for one-leg \(\theta\)-methods for nonlinear infinite-delay-differential equations of the form \(y'(t)=f(t,y(t),y(pt))\), \(t>0\), \(0<p<1\), \(y(0)=\eta\). Two theorems are proved: one concerning a global stability inequality, and a second one concerning the asymptotic stability of one-leg methods.

MSC:

65L20 Stability and convergence of numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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