- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 642318, 21 pages
A Class of New Pouzet-Runge-Kutta-Type Methods for Nonlinear Functional Integro-Differential Equations
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
Received 2 October 2011; Accepted 7 February 2012
Academic Editor: Shaher Momani
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK, 1991.