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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 535979, 9 pages
Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems
1Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
2Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Malaysia
Received 13 January 2013; Accepted 8 March 2013
Academic Editor: Mustafa Bayram
Copyright © 2013 Emran Tohidi 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.
Citations to this Article [12 citations]
The following is the list of published articles that have cited the current article.
- F. Toutounian, and E. Tohidi, “A new Bernoulli matrix method for solving second order linear partial differential equations with the convergence analysis,” Applied Mathematics and Computation, vol. 223, pp. 298–310, 2013.
- D. Baleanu, A. H. Bhrawy, and T. M. Taha, “Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems,” Abstract and Applied Analysis, vol. 2013, pp. 1–10, 2013.
- E. Tohidi, Kh. Erfani, M. Gachpazan, and S. Shateyi, “A New Tau Method for Solving Nonlinear Lane-Emden Type Equations via Bernoulli Operational Matrix of Differentiation,” Journal of Applied Mathematics, vol. 2013, pp. 1–9, 2013.
- Emran Tohidi, Atena Pasban, A. Kilicman, and S. Lotfi Noghabi, “An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems,” Abstract and Applied Analysis, vol. 2013, pp. 1–7, 2013.
- Emran Tohidi, and Adem Kılıçman, “A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation,” Mathematical Problems in Engineering, vol. 2013, pp. 1–9, 2013.
- Emran Tohidi, “Taylor matrix method for solving linear two-dimensional Fredholm integral equations with Piecewise Intervals,” Computational and Applied Mathematics, 2014.
- Emran Tohidi, and Hassan Saberi Nik, “A Bessel Collocation Method for Solving Fractional Optimal Control Problems,” Applied Mathematical Modelling, 2014.
- Emran Tohidi, and Faezeh Toutounian, “Convergence analysis of Bernoulli matrix approach for one-dimensional matrix hyperbolic equations of the first order,” Computers & Mathematics with Applications, 2014.
- Emran Tohidi, M. M. Ezadkhah, and S. Shateyi, “Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014.
- Emran Tohidi, and Mohammad Khorsand Zak, “A New Matrix Approach For Solving Second-Order Linear Matrix Partial Differential Equations,” Mediterranean Journal of Mathematics, 2015.
- M. Alipour, M. A. Vali, and A. H. Borzabadi, “A direct approach for approximate optimal control of integro-differential equations based on homotopy analysis and parametrization method,” IMA Journal of Mathematical Control and Information, pp. dnv061, 2015.
- K. Mamehrashi, and S.A. Yousefi, “A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation,” International Journal of Control, pp. 1–9, 2016.