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Liu, M. Z.; Yang, Z. W.; Xu, Y.

The stability of modified Runge-Kutta methods for the pantograph equation. (English) Zbl 1094.65075

Math. Comput. 75, No. 255, 1201-1215 (2006).
The authors construct a modified Runge-Kutta method and show that it preserves the order of accuracy of the original one. They obtain necessary and sufficient conditions for asymptotic stability of the modified Runge-Kutta method with a variable mesh. Thus the \(\theta\)-methods with \(\frac12\leq\theta\leq1\), the odd stage Gauss-Legendre methods and the even stage Lobatto III A and III B methods become asymptotically stable. Numerical examples are given to illustrate the effectiveness of the method.
Reviewer: Narahari Parhi (Bhubaneswar)

Cited in 14 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
34A34 Nonlinear ordinary differential equations and systems

Keywords:

Runge-Kutta method; asymptotic stability; pantograph equation; \(\theta\)-methods; Gauss-Legendre methods; Lobatto III A and III B methods; numerical examples
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References:

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