Abstract
This paper is concerned with the numerical solution of delay differential equations(DDEs). We focus on the stability behaviour of Runge-Kutta methods for nonlinear DDEs. The new concepts of GR(l)-stability, GAR(l)-stability and weak GAR(l)-stability are further introduced. We investigate these stability properties for (k, l)-algebraically stable Runge-Kutta methods with a piecewise constant or linear interpolation procedure.
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Chengming, H., Hongyuan, F., Shoufu, L. et al. Stability Analysis of Runge-Kutta Methods for Non-Linear Delay Differential Equations. BIT Numerical Mathematics 39, 270–280 (1999). https://doi.org/10.1023/A:1022341929651
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DOI: https://doi.org/10.1023/A:1022341929651