Involve: A Journal of Mathematics

  • Involve
  • Volume 3, Number 4 (2010), 393-404.

A numerical investigation on the asymptotic behavior of discrete Volterra equations with two delays

Immacolata Garzilli, Eleonora Messina, and Antonia Vecchio

Full-text: Open access


We describe a numerical approach to the solution of two-delay Volterra integral equations, and we carry out a nonlinear stability analysis on an interesting test equation by means of a parallel investigation both on the continuous and the discrete problem.

Article information

Involve, Volume 3, Number 4 (2010), 393-404.

Received: 9 July 2010
Revised: 15 September 2010
Accepted: 24 September 2010
First available in Project Euclid: 20 December 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 45M05: Asymptotics 45M10: Stability theory 65R20: Integral equations

Volterra integral equations direct quadrature methods stability double delays


Garzilli, Immacolata; Messina, Eleonora; Vecchio, Antonia. A numerical investigation on the asymptotic behavior of discrete Volterra equations with two delays. Involve 3 (2010), no. 4, 393--404. doi:10.2140/involve.2010.3.393.

Export citation


  • D. Breda, C. Cusulin, M. Iannelli, S. Maset, and R. Vermiglio, “Stability analysis of age-structured population equations by pseudospectral differencing methods”, J. Math. Biol. 54:5 (2007), 701–720.
  • H. Brunner and P. J. van der Houwen, The numerical solution of Volterra equations, vol. 3, CWI Monographs, North-Holland Publishing Co., Amsterdam, 1986.
  • M. Iannelli, Mathematical theory of age-structured population dynamics, Applied Mathematics Monographs (C.N.R), Giardini Editori e Stampatori, Pisa, Italy, 1994.
  • P. Linz, Analytical and numerical methods for Volterra equations, vol. 7, SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1985.
  • E. Messina, E. Russo, and A. Vecchio, “Comparing analytical and numerical solution of a nonlinear two delays integral equations”, technical report RT 342/08, Istituto per le Applicazioni del Calcolo “Mauro Picone”, 2008. To appear on Math. Comp. Simul.
  • E. Messina, E. Russo, and A. Vecchio, “A stable numerical method for Volterra integral equations with discontinuous kernel”, J. Math. Anal. Appl. 337:2 (2008), 1383–1393.
  • E. Messina, E. Russo, and A. Vecchio, “A convolution test equation for double delay integral equations”, J. Comput. Appl. Math. 228:2 (2009), 589–599.
  • E. Messina, Y. Muroya, E. Russo, and A. Vecchio, “Convergence of solutions for two delays Volterra integral equations in the critical case”, Appl. Math. Lett. 23 (2010), 1162–1165.