Copyright © 2012 Chengjian Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

1. C. Zhang and S. Vandewalle, “Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations,” IMA Journal of Numerical Analysis, vol. 24, no. 2, pp. 193–214, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
2. C. Zhang and S. Vandewalle, “General linear methods for Volterra integro-differential equations with memory,” SIAM Journal on Scientific Computing, vol. 27, no. 6, pp. 2010–2031, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
3. Y. Yu, L. Wen, and S. Li, “Nonlinear stability of Runge-Kutta methods for neutral delay integro-differential equations,” Applied Mathematics and Computation, vol. 191, no. 2, pp. 543–549, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
4. C. Zhang, T. Qin, and J. Jin, “An improvement of the numerical stability results for nonlinear neutral delay-integro-differential equations,” Applied Mathematics and Computation, vol. 215, no. 2, pp. 548–556, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
5. C. Zhang, T. Qin, and J. Jin, “The extended Pouzet-Runge-Kutta methods for nonlinear neutral delay-integro-differential equations,” Computing, vol. 90, no. 1-2, pp. 57–71, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
6. H. Brunner and R. Vermiglio, “Stability of solutions of delay functional integro-differential equations and their discretizations,” Computing, vol. 71, no. 3, pp. 229–245, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
7. H. Brunner, “The discretization of neutral functional integro-differential equations by collocation methods,” Zeitschrift für Analysis und ihre Anwendungen, vol. 18, no. 2, pp. 393–406, 1999.
8. H. Brunner, “High-order collocation methods for singular Volterra functional equations of neutral type,” Applied Numerical Mathematics, vol. 57, no. 5-7, pp. 533–548, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
9. C. T. H. Baker, “A perspective on the numerical treatment of Volterra equations,” Journal of Computational and Applied Mathematics, vol. 125, no. 1-2, pp. 217–249, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
10. H. Brunner, Collocation Methods for Volterra Integral and Related Functional Differential Equations, vol. 15 of Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, UK, 2004. View at Publisher · View at Google Scholar
11. H. Brunner and P. J. van der Houwen, The Numerical Solution of Volterra Equations, vol. 3 of CWI Monographs, North-Holland, Amsterdam, The Netherlands, 1986.
12. W. Wang, “A generalized Halanay inequality for stability of nonlinear neutral functional differential equations,” Jurnal of Inequalities and Applications, vol. 2010, Article ID 475019, 16 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. L. Wen, Y. Yu, and W. Wang, “Generalized Halanay inequalities for dissipativity of Volterra functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 347, no. 1, pp. 169–178, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
14. E. Hairer and G. Wanner, Solving Ordinary Differential Equations. II: Stiff and Differential-Algebraic Problems, vol. 14 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 2nd edition, 1996. View at Zentralblatt MATH
15. Dahlquist G. and Jeltsch R., “Generalized disks of contractivity for ex-plicit and implicit Runge-Kutta methods,” TRITA-NA Report 7906, The Royal Institute of Technology, Stockholm, Sweden, 1979.
16. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK, 1991.