Abstract
Stability properties of numerical methods for Volterra integral equations with lagging argument are considered. Some suitable definitions for the stability of the numerical methods are included, and plots of the stability regions for particular cases are included.
Similar content being viewed by others
References
S. Amni, C. T. H. Baker, P. J. van der Houwen, and P. H. M. Walkenfelt,Stability analysis of numerical methods for Volterra integral equations with polynomial convolution kernels, J. Integral Equations, 5 (1983), pp. 73–92.
P. H. M. Walkenfelt,On the numerical stability of reducible quadrature methods for second kind Volterra integral equations, Z. Angew Math. Mech., 61 (1981), pp. 399–401.
D. Morugim,Impulsive Structures with Delayed Feedback, Moscow, 1961 (in Russian).
D. Morugim,Resistence of impact with retarded inverse connections, Sovetskoe Radio (1961) (in Russian).
J. M. Bownds, J. M. Cushing, and R. Schutte,Existence, uniqueness and extendibility of solutions of Volterra integral systems with multiple variable lags, Funkcial. Ekvac., 19 (1976), pp. 101–111.
B. Cahlon, J. Nachman, and D. Schmidt,Numerical solution of Volterra integral equations with delay arguments, J. Integral Equations, 7 (1984), pp. 191–208.
P. H. M. Walkenfelt,The construction of reducible quadrature rules for Volterra integral and integro-differential equations, IMA J. Numer. Anal., 2 (1982), pp. 131–152.
J. D. Lambert,Computational Methods in Ordinary Differential Equations, Wiley, New York, 1973.
P. H. M. Walkenfelt,Linear multisteps and the construction of quadrature formulae for Volterra integral and integro-differential equations, Report NW 76/79, Math. Centrum, Amsterdam, 1979.
C. T. H. Baker and M. S. Keech,Stability regions in the numerical treatment of Volterra integral equations, SIAM J. Numer. Anal., 15 (1978), pp. 394–417.
R. Bellman and K. L. Cooke,Differential-Difference Equations, Academic Press, New York, 1963.
V. L. Bakke and Z. Jackiewicz,Stability of reducible quadrature methods for Volterra integral equations of the second kind, Numer. Math. (1985), pp. 159–173.
M. Marsden,Geometry of Polynomials, Amer. Mathematical Soc., Providence, RI., 1966.
G. Dahlquist,A special stability problem for linear multistep methods, BIT, 3 (1963), pp. 27–43.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cahlon, B. On the stability of Volterra integral equations with a lagging argument. Bit Numer Math 35, 19–29 (1995). https://doi.org/10.1007/BF01732976
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01732976