- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- 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 2013 (2013), Article ID 416757, 8 pages
Numerical Solution of Nonlinear Fredholm Integrodifferential Equations by Hybrid of Block-Pulse Functions and Normalized Bernstein Polynomials
General Required Courses Department, Jeddah Community College, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Received 24 April 2013; Accepted 1 September 2013
Academic Editor: Santanu Saha Ray
Copyright © 2013 S. H. Behiry. 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.
- M. Dehghan and A. Saadatmandi, “Chebyshev finite difference method for Fredholm integro-differential equation,” International Journal of Computer Mathematics, vol. 85, no. 1, pp. 123–130, 2008.
- Z. Lackiewicz, M. Rahman, and B. D. Welfert, “Numerical solution of a Fredholm integro-differential equation modelling neural networks,” Applied Numerical Mathematics, vol. 56, no. 3-4, pp. 423–432, 2006.
- M. Lakestani, M. Razzaghi, and M. Dehghan, “Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations,” Mathematical Problems in Engineering, vol. 2006, Article ID 96184, 12 pages, 2006.
- S. H. Behiry and H. Hashish, “Wavelet methods for the numerical solution of Fredholm integro-differential equations,” International Journal of Applied Mathematics, vol. 11, no. 1, pp. 27–35, 2002.
- S. Islam, I. Aziz, and M. Fayyaz, “A new approach for numerical solution of integro-differential equations via Haar wavelets,” International Journal of Computer Mathematics, 2013.
- Y. Ordokhani, “An application of Walsh functions for Fredholm-Hammerstein integro-differential equations,” International Journal of Contemporary Mathematical Sciences, vol. 5, no. 22, pp. 1055–1063, 2010.
- S. Yeganeh, Y. Ordokhani, and A. Saadatmandi, “A sinc-collocation method for second-order boundary value problems of nonlinear integro-differential equation,” Journal of Information and Computing Science, vol. 7, no. 2, pp. 151–160, 2012.
- Sh. S. Behzadi, S. Abbasbandy, T. Allahviranloo, and A. Yildirim, “Application of homotopy analysis method for solving a class of nonlinear Volterra-Fredholm integro-differential equations,” The Journal of Applied Analysis and Computation, vol. 2, no. 2, pp. 127–136, 2012.
- S. H. Behiry and S. I. Mohamed, “Solving high-order nonlinear Volterra-Fredholm integro-differential equations by differential transform method,” Natural Science, vol. 4, no. 8, pp. 581–587, 2012.
- K. Maleknejad, B. Basirat, and E. Hashemizadeh, “Hybrid Legendre polynomials and block-pulse functions approach for nonlinear Volterra-Fredholm integro-differential equations,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2821–2828, 2011.
- R. Ezzati and S. Najafalizadeh, “Application of Chebyshev polynomials for solving nonlinear Volterra-Fredholm integral equations system and convergence analysis,” Indian Journal of Science and Technology, vol. 5, no. 2, pp. 2060–2064, 2012.
- A. H. Bhrawy, E. Tohidi, and F. Soleymani, “A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals,” Applied Mathematics and Computation, vol. 219, no. 2, pp. 482–497, 2012.
- Z. H. Jiang and W. Schaufelberger, Block Pulse Functions and Their Applications in Control Systems, Springer, Berlin, Germany, 1992.
- S. A. Yousefi, Z. Barikbin, and M. Dehghan, “Ritz-Galerkin method with Bernstein polynomial basis for finding the product solution form of heat equation with non-classic boundary conditions,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22, no. 1, pp. 39–48, 2012.
- K. Maleknejad, E. Hashemizadeh, and B. Basirat, “Computational method based on Bernstein operational matrices for nonlinear Volterra-Fredholm-Hammerstein integral equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 52–61, 2012.
- G. Tachev, “Pointwise approximation by Bernstein polynomials,” Bulletin of the Australian Mathematical Society, vol. 85, no. 3, pp. 353–358, 2012.
- Y. Ordokhani and S. Davaei far, “Application of the Bernstein polynomials for solving the nonlinear Fredholm integro-differential equations,” Journal of Applied Mathematics and Bioinformatics, vol. 1, no. 2, pp. 13–31, 2011.
- K. Jalaei, M. Zarebnia, and M. M. Chalaki, “Development of the sinc method for nonlinear integro-differential eequations,” Australian Journal of Basic and Applied Sciences, vol. 4, no. 11, pp. 5508–5515, 2010.