Stability of a class of Runge-Kutta methods for a family of pantograph equations of neutral type

Applied Mathematics and Computation

Volumn 181, Issue 2, 2006, Pages 1170-1181

  Zhao, J J ^a   Xu, Y ^a   Wang, H X ^a   Liu, M Z ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Numerical methods; Pantograph equations; Stability

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; FUNCTIONS; NUMERICAL METHODS;

GAUSS-LEGENDRE METHODS; PANTOGRAPH EQUATIONS; PROPORTIONAL DELAYS;

RUNGE KUTTA METHODS;

EID: 33750459376     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.01.084     Document Type: Article

References (15)

1. Bellen A., Guglielmi N., and Torelli L. Asymptotic stability properties of θ-methods for the pantograph equation. Appl. Numer. Math. 24 (1997) 279-293
2. Bellen A., and Zennaro M. Numerical Methods for Delay Differential Equations (2003), Oxford University Press, New York
3. Dekker K., and Verwer J.G. Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations (1984), North-Holland, Amsterdam
4. Feldstein M.A., and Grafton C.K. Experimental mathematics: an application to retarded ordinary differential equations with infinite lag. Proc. 1968 ACM National Conference (1968), Brandon Systems Press 67-71
5. Horn R.A., and Johnson C.R. Matrix Analysis (1985), Cambridge University Press, Cambridge
6. Iserles A. On the generalized pantograph functional-differential equation. Eur. J. Appl. Math. 4 (1993) 1-38
7. Iserles A. Exact and discretized stability of the pantograph equation. Appl. Numer. Math. 24 (1997) 295-308
8. Iserles A., and Liu Y.K. On the neutral functional-differential equations with proportional delays. J. Math. Anal. Appl. 207 (1997) 73-95
9. Koto T. Stability of Runge-Kutta methods for the generalized pantograph equation. Numer. Math. 84 (1999) 233-247
10. Liu Y.K. Stability of θ-methods for neutral functional-differential equations. Numer. Math. 70 (1995) 473-485
11. Liu Y.K. On the θ-method for delay differential equations with infinite lag. J. Comput. Appl. Math. 71 (1996) 177-190
12. Liu Y.K. Numerical investigation of the pantograph equation. Appl. Numer. Math. 24 (1997) 309-317
13. Xu Y., and Liu M.Z. H-stability of Runge-Kutta methods with general variable stepsize for pantograph equation. Appl. Math. Comput. 148 (2004) 881-892
14. Xu Y., Zhao J.J., and Liu M.Z. H-stability of Runge-Kutta methods with variable stepsize for system of pantograph equations. J. Comput. Math. 22 (2004) 727-734
15. Zhang C.J., and Sun G. Boundedness and asymptotic stability of multistep methods for generalized pantograph equations. J. Comput. Math. 22 (2004) 447-456