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Asymptotic stability analysis of Runge-Kutta methods for differential-algebraic equations with multiple delays. (English) Zbl 1472.65086

Summary: This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge-Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge-Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge-Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge-Kutta methods.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

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