Summary
A completion ofB-convergence results of Lobatto IIIC schemes is presented. In particular, it is shown that Lobatto IIIC schemes with more than two stages areB-convergent when applied to IVPs with a negative one-sided Lipschitz constantm; they are notB-convergent, however, for IVPs with a non-negativem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Burrage, K., Butcher, J.C.: Non-linear stability of a general class of differential equation methods. Dept. of Math., Univ. of Auckland, Rep. No. 142 (1979)
Dekker, K., Hairer, E.: A necessary condition for BSI-stability. BIT25, 285–288 (1985)
Dekker, K., Verwer, J.G.: Stability of Runge-Kutta methods for stiff nonlinear differential equations. Amsterdam-New York-Oxford: North-Holland 1984
Frank, R., Schneid, J., Ueberhuber, C.W.: The concept ofB-convergence. SIAM J. Numer. Anal.18, 753–780 (1981)
Frank, R., Schneid, J., Ueberhuber, C.W.: Stability properties of implicit Runge-Kutta methods. SIAM J. Numer. Anal.22, 497–515 (1985)
Frank, R., Schneid, J., Ueberhuber, C.W.: Order results for implicit Runge-Kutta methods applied to stiff systems. SIAM J. Numer. Anal.22, 515–534 (1985)
Schneid, J.: A new approach to optimalB-convergence. Computing38, 33–42 (1987)
Spijker, M.N.: The relevance of algebraic stability in implicit Runge-Kutta methods. In: Strehmel, K. (ed.), Num. Treatment of Diff. Equations, pp. 150–164. Leipzig: Teubner 1986
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schneid, J. B-Convergence of Lobatto IIIC formulas. Numer. Math. 51, 229–235 (1987). https://doi.org/10.1007/BF01396751
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01396751