The GPL-stability of Rosenbrock methods for delay differential equation

This paper deals with the stability analysis of the Rosenbrock method for the numerical solution of delay differential equation. The stability behavior of Rosenbrock method is analyzed for the solutions of linear test equation. We will give that the Rosenbrock method is GPL-stable if and only if it is L-stable.

[1]  Zhang Chengjian,et al.  Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations , 1997 .

[2]  Hongjiong Tian,et al.  The asymptotic stability of one-parameter methods for neutral differential equations , 1994 .

[3]  LI Shou-fu Asymptotic Stability of Rosenbrock Methods for Delay Differential Equations , 2002 .

[4]  Chengming Huang,et al.  Stability and error analysis of one-leg methods for nonlinear delay differential equations , 1999 .

[5]  F. Krogh,et al.  Solving Ordinary Differential Equations , 2019, Programming for Computations - Python.

[6]  V. Barwell,et al.  Special stability problems for functional differential equations , 1975 .

[7]  J. Lambert Computational Methods in Ordinary Differential Equations , 1973 .

[8]  Marino Zennaro,et al.  Stability analysis of one-step methods for neutral delay-differential equations , 1988 .

[9]  K. J. in 't Hout,et al.  A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations , 1992 .

[10]  E. Hairer,et al.  Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .

[11]  Guang-Da Hu,et al.  Stability analysis of numerical methods for systems of neutral delay-differential equations , 1995 .

[12]  K. J. in 't Hout,et al.  On the stability of adaptations of Runge-Kutta methods to systems of delay differential equations , 1996 .

[13]  M. N. Spijker,et al.  The stability of the θ-methods in the numerical solution of delay differential equations , 1990 .

[14]  R. Piché An L-stable Rosenbrock method for step-by-step time integration in structural dynamics , 1995 .

[15]  Toshiyuki Koto,et al.  A stability property ofA-stable natural Runge-Kutta methods for systems of delay differential equations , 1994 .