- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- 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
Advances in Numerical Analysis
Volume 2012 (2012), Article ID 868279, 14 pages
Solution of Nonlinear Volterra-Fredholm Integrodifferential Equations via Hybrid of Block-Pulse Functions and Lagrange Interpolating Polynomials
Department of Mathematical Sciences, Isfahan University of Technology, P.O. Box 8415683111, Isfahan, Iran
Received 22 May 2012; Accepted 8 November 2012
Academic Editor: Alfredo Bermudez De Castro
Copyright © 2012 Hamid Reza Marzban and Sayyed Mohammad Hoseini. 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.
- A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2nd edition, 2008.
- P. J. Van der Houwen and B. P. Sommeijer, “Euler-Chebyshev methods for integro-differential equations,” Applied Numerical Mathematics, vol. 24, no. 2-3, pp. 203–218, 1997.
- W. H. Enright and M. Hu, “Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay,” Applied Numerical Mathematics, vol. 24, no. 2-3, pp. 175–190, 1997.
- P. Darania and A. Ebadian, “A method for the numerical solution of the integro-differential equations,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 657–668, 2007.
- A. Shidfar, A. Molabahrami, A. Babaei, and A. Yazdanian, “A series solution of the nonlinear Volterra and Fredholm integro-differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 2, pp. 205–215, 2010.
- J. E. Mittler, B. Sulzer, A. U. Neumann, and A. S. Perelson, “Influence of delayed viral production on viral dynamics in HIV-1 infected patients,” Mathematical Biosciences, vol. 152, no. 2, pp. 143–163, 1998.
- S. Yalcinbas and M. Sezer, “The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials,” Applied Mathematics and Computation, vol. 112, no. 2-3, pp. 291–308, 2000.
- K. Maleknejad and Y. Mahmoudi, “Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations,” Applied Mathematics and Computation, vol. 145, no. 2-3, pp. 641–653, 2003.
- P. Darania and K. Ivaz, “Numerical solution of nonlinear Volterra-Fredholm integro-differential equations,” Computers & Mathematics with Applications, vol. 56, no. 9, pp. 2197–2209, 2008.
- F. Bloom, “Asymptotic bounds for solutions to a system of damped integro-differential equations of electromagnetic theory,” Journal of Mathematical Analysis and Applications, vol. 73, no. 2, pp. 524–542, 1980.
- K. Holmåker, “Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones,” SIAM Journal on Mathematical Analysis, vol. 24, no. 1, pp. 116–128, 1993.
- L. K. Forbes, S. Crozier, and D. M. Doddrell, “Calculating current densities and fields produced by shielded magnetic resonance imaging probes,” SIAM Journal on Applied Mathematics, vol. 57, no. 2, pp. 401–425, 1997.
- A. Akyüz and M. Sezer, “A Taylor polynomial approach for solving high-order linear Fredholm integro-differential equations in the most general form,” International Journal of Computer Mathematics, vol. 84, no. 4, pp. 527–539, 2007.
- I. P. Streltsov, “Application of Chebyshev and Legendre polynomials on discrete point set to function interpolation and solving Fredholm integral equations,” Computer Physics Communications, vol. 126, no. 1-2, pp. 178–181, 2000.
- E. Babolian, Z. Masouri, and S. Hatamzadeh-Varmazyar, “Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions,” Computers & Mathematics with Applications, vol. 58, no. 2, pp. 239–247, 2009.
- N. Bildik, A. Konuralp, and S. Yalçınbaş, “Comparison of Legendre polynomial approximation and variational iteration method for the solutions of general linear Fredholm integro-differential equations,” Computers & Mathematics with Applications, vol. 59, no. 6, pp. 1909–1917, 2010.
- S.-Q. Wang and J.-H. He, “Variational iteration method for solving integro-differential equations,” Physics Letters A, vol. 367, no. 3, pp. 188–191, 2007.
- J. I. Ramos, “Iterative and non-iterative methods for non-linear Volterra integro-differential equations,” Applied Mathematics and Computation, vol. 214, no. 1, pp. 287–296, 2009.
- M. Dehghan and R. Salehi, “The numerical solution of the non-linear integro-differential equations based on the meshless method,” Journal of Computational and Applied Mathematics, vol. 236, no. 9, pp. 2367–2377, 2012.
- H. R. Marzban, S. M. Hoseini, and M. Razzaghi, “Solution of Volterra's population model via block-pulse functions and Lagrange-interpolating polynomials,” Mathematical Methods in the Applied Sciences, vol. 32, no. 2, pp. 127–134, 2009.
- C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer, New York, NY, USA, 1987.
- H. R. Marzban, H. R. Tabrizidooz, and M. Razzaghi, “A composite collocation method for the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1186–1194, 2011.
- E. L. Ortiz, “The tau method,” SIAM Journal on Numerical Analysis, vol. 6, pp. 480–492, 1969.
- G. Ebadi, M. Y. Rahimi-Ardabili, and S. Shahmorad, “Numerical solution of the nonlinear Volterra integro-differential equations by the tau method,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1580–1586, 2007.