- 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 2013 (2013), Article ID 198926, 11 pages
Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications
1Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
2Center of Excellence on Modelling and Control Systems, Ferdowsi University of Mashhad, Mashhad, Iran
3Department of Mathematics, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia
Received 1 January 2013; Revised 4 March 2013; Accepted 4 March 2013
Academic Editor: Carlos Vazquez
Copyright © 2013 F. Toutounian et al. 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.
- G. P. Rao and K. R. Palaisamy, “Walsh stretch matrices and functional differential equations,” IEEE Transactions on Automatic Control, vol. 27, no. 1, pp. 272–276, 1982.
- C. Hwang and Y. P. Shih, “Laguerre series solution of a functional differential equation,” International Journal of Systems Science, vol. 13, no. 7, pp. 783–788, 1982.
- M. Sezer, S. Yalçinbaş, and M. Gülsu, “A Taylor polynomial approach for solving generalized pantograph equations with nonhomogenous term,” International Journal of Computer Mathematics, vol. 85, no. 7, pp. 1055–1063, 2008.
- S. Yalçinbaç, M. Aynigül, and M. Sezer, “A collocation method using Hermite polynomials for approximate solution of pantograph equations,” Journal of the Franklin Institute, vol. 348, no. 6, pp. 1128–1139, 2011.
- M. S. Corrington, “Solution of differential and integral equations with walsh functions,” IEEE Transactions on Circuit Theory, vol. 20, no. 5, pp. 470–476, 1973.
- C. F. Chen and C. H. Hsiao, “Time-domain synthesis via walsh functions,” Proceedings of the Institution of Electrical Engineers, vol. 122, no. 5, pp. 565–570, 1975.
- C. F. Chen and C. H. Hsiao, “Walsh series analysis in optimal control,” International Journal of Control, vol. 21, no. 6, pp. 881–897, 1975.
- N. S. Hsu and B. Cheng, “Analysis and optimal control of time-varying linear systems via block-pulse functions,” International Journal of Control, vol. 33, no. 6, pp. 1107–1122, 1981.
- C. Hwang and Y. P. Shih, “Parameter identification via laguerre polynomials,” International Journal of Systems Science, vol. 13, no. 2, pp. 209–217, 1982.
- I. R. Horng and J. H. Chou, “Shifted chebyshev direct method for solving variational problems,” International Journal of Systems Science, vol. 16, no. 7, pp. 855–861, 1985.
- R. Y. Chang and M. L. Wang, “Shifted Legendre direct method for variational problems,” Journal of Optimization Theory and Applications, vol. 39, no. 2, pp. 299–307, 1983.
- G. T. Kekkeris and P. N. Paraskevopoulos, “Hermite series approach to optimal control,” International Journal of Control, vol. 47, no. 2, pp. 557–567, 1988.
- M. Razzaghi and M. Razzaghi, “Fourier series direct method for variational problems,” International Journal of Control, vol. 48, no. 3, pp. 887–895, 1988.
- E. H. Doha, A. H. Bhrawy, and M. A. Saker, “Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations,” Applied Mathematics Letters, vol. 24, no. 4, pp. 559–565, 2011.
- P. N. Paraskevopoulos, P. G. Sklavounos, and G. C. Georgiou, “The operational matrix of integration for Bessel functions,” Journal of the Franklin Institute, vol. 327, no. 2, pp. 329–341, 1990.
- 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.
- A. Akyüz-Dascioglu, “Chebyshev polynomial approximation for high-order partial differential equations with complicated conditions,” Numerical Methods for Partial Differential Equations, vol. 25, no. 3, pp. 610–621, 2009.
- M. Gülsu, B. Gürbüz, Y. Öztürk, and M. Sezer, “Laguerre polynomial approach for solving linear delay difference equations,” Applied Mathematics and Computation, vol. 217, no. 15, pp. 6765–6776, 2011.
- M. Sezer, S. Yalçinbaş, and N. Şahin, “Approximate solution of multi-pantograph equation with variable coefficients,” Journal of Computational and Applied Mathematics, vol. 214, no. 2, pp. 406–416, 2008.
- E. Tohidi, “Legendre approximation for solving linear HPDEs and comparison with taylor and bernoulli matrix methods,” Applied Mathematics, vol. 3, pp. 410–416, 2012.
- E. Tohidi, A. H. Bhrawy, and Kh. Erfani, “A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation,” Applied Mathematical Modelling, vol. 37, no. 6, pp. 4283–4294, 2013.
- E. Tohidi, “Bernoulli matrix approach for solving two dimensional linear hyperbolic partial differential equations with constant coefficients,” American Journal of Computational and Applied Mathematics, vol. 2, no. 4, pp. 136–139, 2012.
- F. Toutounian, E. Tohidi, and S. Shateyi, “A collocation method based on Bernoulli operational matrix for solving high order linear complex differential equations in a rectangular domain,” Abstract, Applied, Analysis, Article ID 823098, 2013.
- S. A. Yousefi and M. Behroozifar, “Operational matrices of Bernstein polynomials and their applications,” International Journal of Systems Science, vol. 41, no. 6, pp. 709–716, 2010.
- S. Yuzbasi, Bessel polynomial solutions of linear differential, integral and integro-differential equations [M.S. thesis], Graduate School of Natural and Applied Sciences, Mugla University, 2009.
- S. Yuzbasi, “A numerical approximation based on the Bessel functions of first kind for solutions of Riccati type differen- tialdifference equations,” Computers & Mathematics with Applications, vol. 64, no. 6, pp. 1691–1705, 2012.
- S. Yuzbasi and M. Sezer, “An improved Bessel collocation method with a residual error function to solve a class of LaneEmden differential equations,” Computer Modeling, vol. 57, pp. 1298–1311, 2013.
- S. Yuzbasi, M. Sezer, and B. Kemanci, “Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method,” Applied Mathematical Modelling, vol. 37, pp. 2086–2101, 2013.
- Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia, Pa, USA, 2nd edition, 2003.
- O. R. N. Samadi and E. Tohidi, “The spectral method for solving systems of Volterra integral equations,” Journal of Applied Mathematics and Computing, vol. 40, no. 1-2, pp. 477–497, 2012.
- E. Tohidi and O. R. N. Samadi, “Optimal control of nonlinear Volterra integral equations via Legendre polynomials,” IMA Journal of Mathematical Control and Information, vol. 30, no. 1, pp. 67–83, 2013.