New stability results for Runge-Kutta methods adapted to delay differential equations

Applied Numerical Mathematics

Volumn 34, Issue 2, 2000, Pages 293-308

  Van Den Heuvel, Guido ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; FUNCTIONS; INITIAL VALUE PROBLEMS; INTERPOLATION; LINEAR EQUATIONS; MATRIX ALGEBRA; PROBLEM SOLVING; VECTORS;

DELAY DIFFERENTIAL EQUATIONS; RESOLVENT CONDITIONS;

RUNGE KUTTA METHODS;

EID: 0034229834     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00134-8     Document Type: Article

References (14)

1. [1] K. Burrage, W.H. Hundsdorfer, J.G. Verwer, A study of B-convergence of Runge-Kutta methods, Computing 36 (1986) 17-34.
2. [2] J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations, Wiley, New York.
3. [3] P. Henrici, Applied and Computational Complex Analysis, Vol. 1, Wiley, New York, 1974.
4. [4] E. Hairer, G. Wanner, Solving Ordinary Differential Equations II, Springer, Berlin.
5. [5] K.J. in't Hout, A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations, BIT 32 (1992) 634-649.
6. [6] K.J. in't Hout, On the stability of adaptations of Runge-Kutta methods to systems of delay differential equations, Appl. Numer. Math. 22 (1996) 237-250.
7. [7] K.J. in't Hout, Stability analysis of Runge-Kutta methods for systems of delay differential equations, IMA J. Numer. Anal. 17 (1997) 17-27.
8. [8] M.Z. Liu, M.N. Spijker, The stability of the θ-methods in the numerical solution of delay differential equations, IMA J. Numer. Anal. 10 (1990) 31-48.
9. [9] M.N. Spijker, Numerical stability, resolvent conditions and delay differential equations, Appl. Numer. Math. 24 (1997) 233-246.
10. [10] M.N. Spijker, F.A.J. Straetemans, Stability estimates for families of matrices of non-uniformly bounded order, Linear Algebra Appl. 239 (1996) 77-102.
11. [11] G. Strang, Trigonometric polynomials and difference methods of maximum accuracy, J. Math. Phys. 41 (1962) 147-154.
12. [12] E.G. Van den Heuvel, Using resolvent conditions to obtain new stability results for θ-methods for delay differential equations, IMA J. Numer. Anal., to appear.
13. [13] J.L.M. Van Dorsselaer, J.F.B.M. Kraaijevanger, M.N. Spijker, Linear stability analysis in the numerical solution of initial value problems, Acta Numer. (1993) 199-237.
14. [14] M. Zennaro, P-stability properties of Runge-Kutta methods for delay differential equations, Numer. Math. 49 (1986) 305-318.