Abstract
The concept of (A 0,S)-stability, for numerical methods approximating solutions of Volterra integral equations, is formally defined. New stability polynomials for the recent multi-lag type methods are obtained. (A 0, 1)-stability of these and other methods employing reducible quadrature rules are also investigated.
Similar content being viewed by others
References
S. Amini,Analysis of stability behaviour in the treatment of certain Volterra integral equations, PhD Thesis University of Manchester (1980).
S. Amini,Stability analysis of methods employing reducible quadrature rules for solutions of Volterra integral equations, Report No: CS-81-02, School of Mathematics, University of Bristol, England (1981).
S. Amini, C. T. H. Baker, P. J. Van der Houwen and P. H. M. Wolkenfelt,Stability analysis of numerical methods for Volterra integral equations with polynomial convolution kernels, Report NW 109/81, Mathematisch Centrum, Amsterdam (to appear in the Journal of Integral Equations) (1981).
C. T. H. Baker,The Numerical Treatment of Integral Equations, Oxford Clarendon Press (1977).
C. T. H. Baker and M. S. Keech,Stability regions in the numerical treatment of Volterra integral equations, SIAM J. Numer. Anal. 15 (1978). 395–417.
H. Brunner, S. P. Nørsett and P. H. M. Wolkenfelt,On V 0-stability of numerical methods for Volterra integral equations of the second kind, Report NW 84/80, Mathematisch Centrum, Amsterdam (1980).
Z. B. Tsalyuk,Volterra integral equations, Journal of Soviet Mat. Vol 12 (1977), 715–757 (translated from Itogi Naukii Tekhniki, Matematicheskii Analiz. Vol 15 (1977), 131–198).
P. J. Van der Houwen,Convergence and stability analysis of Runge-Kutta type methods for Volterra integral equations of the second kind, Report NW 83/80, Mathematisch Centrum, Amsterdam (1980).
P. J. Van der Houwen,Convergence and stability results in Runge-Kutta type methods for Volterra integral equations of the second kind, BIT 20 (1980), 375–377.
P. H. M. Wolkenfelt,Stability analysis of reducible quadrature methods for Volterra integral equations of the second kind, Report NW 79/80, Mathematisch Centrum, Amsterdam (1980).
P. H. M. Wolkenfelt,Modified multi-lag methods for Volterra functional equations, Report NW 108/81, Mathematisch Centrum, Amsterdam (1981).
P. H. M. Wolkenfelt,The numerical analysis of reducible quadrature methods for Volterra integral and integro-differential equation, PhD Thesis, Mathematisch Centrum, Amsterdam (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Amini, S. Stability analysis of methods employing reducible rules for Volterra integral equations. BIT 23, 322–328 (1983). https://doi.org/10.1007/BF01934461
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01934461