Preservation of oscillations of the Runge-Kutta method for equation \(x'(t)+ax(t)+a_1x([t - 1])=0\). (English) Zbl 1189.65143

Liu, M. Z.; Gao, J. F.; Yang, Z. W.

Comput. Math. Appl. 58, No. 6, 1113-1125 (2009).

Summary: The paper deals with the preservation of oscillations of the Runge-Kutta method for equation \(x'(t)+ax(t)+a_{1}x([t - 1])=0\). It is proved that oscillations of the analytic solution are preserved by the Runge-Kutta method. Special interpolation functions of the numerical solutions are given. It turns out that zeros of the interpolation function of the numerical solution converge to ones of the analytic solution with the same order of accuracy as that of the corresponding Runge-Kutta method. Some numerical experiments are presented.

MSC:

65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L03	Numerical methods for functional-differential equations

Keywords:

oscillation; numerical solution; delay differential equation; piecewise constant; interpolation function

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