Discretized stability and error growth of the nonautonomous pantograph equation.(English)Zbl 1080.65068

The paper deals with stability properties of Runge-Kutta methods for the pantograph equation $y^\prime(t) = f(t,y(t),y(qt),y^\prime(qt)),\quad t > 0,$
$y(0) = y_0.$ The authors obtain sufficient and necessary conditions for the asymptotic stability of the numerical solution and an upper bound for the error growth is obtained.

MSC:

 65L20 Stability and convergence of numerical methods for ordinary differential equations 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L70 Error bounds for numerical methods for ordinary differential equations 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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