An analytic proof of numerical stability of Gaussian collocation for delay differential

Nicola Guglielmi

Bollettino dell'Unione Matematica Italiana (2000)

  • Volume: 3-B, Issue: 1, page 95-116
  • ISSN: 0392-4041

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Guglielmi, Nicola. "An analytic proof of numerical stability of Gaussian collocation for delay differential." Bollettino dell'Unione Matematica Italiana 3-B.1 (2000): 95-116. <http://eudml.org/doc/195857>.

@article{Guglielmi2000,
author = {Guglielmi, Nicola},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {asymptotic stability; delay differential equations; Gaussian collocation methods; hypergeometric series; order stars},
language = {eng},
month = {2},
number = {1},
pages = {95-116},
publisher = {Unione Matematica Italiana},
title = {An analytic proof of numerical stability of Gaussian collocation for delay differential},
url = {http://eudml.org/doc/195857},
volume = {3-B},
year = {2000},
}

TY - JOUR
AU - Guglielmi, Nicola
TI - An analytic proof of numerical stability of Gaussian collocation for delay differential
JO - Bollettino dell'Unione Matematica Italiana
DA - 2000/2//
PB - Unione Matematica Italiana
VL - 3-B
IS - 1
SP - 95
EP - 116
LA - eng
KW - asymptotic stability; delay differential equations; Gaussian collocation methods; hypergeometric series; order stars
UR - http://eudml.org/doc/195857
ER -

References

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  2. BELLMANN, R. and COOKE, K. L., Differential difference equations, Academic Press, New York, 1963. Zbl0105.06402MR147745
  3. BELLEN, A., One-step collocation for delay differential equations, J. Comput. Appl. Math., 10 (1984), 275-283. Zbl0538.65047MR755804
  4. DEKKER, K., KRAAIJEVANGER, J. F. B. M. and SPIJKER, M. N., The order of B-convergence of the Gaussian Runge-Kutta method, Computing, 36 (1986), 35-41. Zbl0565.65040MR832928
  5. GUGLIELMI and E. HAIRER, N., Order stars and stability for delay differential equations, Numer. Math., 83(3) (1999), 371-383. Zbl0937.65079MR1715581
  6. GUGLIELMI, N., On the asymptotic stability properties of Runge-Kutta methods for delay differential equations, Numer. Math., 77(4) (1997), 467-485. Zbl0885.65092MR1473392
  7. HAIRER, E., Constructive characterization of A-stable approximations to exp z and its connection with algebraically stable Runge-Kutta methods, Numer. Math, 39 (1982), 247-258. Zbl0493.65035MR669320
  8. HENRICI, P., Applied and Computational Complex Analysis, vol. 1, Wiley, New York, 1974. Zbl0313.30001MR372162
  9. HAIRER, E. and WANNER, G., Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics, 14, Springer-Verlag, Berlin, 2nd edition, 1996. Zbl0729.65051MR1439506
  10. ISERLES, A. and NØRSETT, S. P., Order Stars, Chapman & Hall, London, 1991. Zbl0743.65062
  11. KUANG, Y., Delay Differential Equations with Application in Population Dynamics, Academic Press, Boston, 1993. Zbl0777.34002MR1218880
  12. SLATER, L. J., Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966. Zbl0135.28101MR201688
  13. ZENNARO, M., On the P-stability of one-step collocation for delay differential equations, ISNM, 74 (1985), 334-343. Zbl0558.65054MR899103

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