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Wang, Wan-Sheng; Li, Shou-Fu; Su, Kai

Nonlinear stability of Runge-Kutta methods for neutral delay differential equations. (English) Zbl 1144.65054

J. Comput. Appl. Math. 214, No. 1, 175-185 (2008).
The stability properties of Runge-Kutta methods for the initial value problem in nonlinear neutral delay differential equations (NDDEs) is studied. The new concepts of GS(1)-stability, GAS(1)-stability and weak GAS(1)-stability of Runge-Kutta methods for NDDEs are introduced, and it is shown that \((k,l)\)-algebraically stable Runge-Kutta methods with piecewise linear interpolation are GS(1), GAS(1)- and Weakly GAS(1)-stable. Two numerical examples are given which confirm the results.
Reviewer: M. Gousidou-Koutita (Thessaloniki)

Cited in 32 Documents

MSC:

65L20 Stability and convergence of numerical methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34K40 Neutral functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)

Keywords:

nonlinear neutral delay differential equations; Runge-Kutta methods; numerical stability; algebraic stability; initial value problem; numerical examples
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References:

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