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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 823098, 12 pages
A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain
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, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa
Received 19 November 2012; Accepted 14 February 2013
Academic Editor: Douglas Anderson
Copyright © 2013 Faezeh 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.
Citations to this Article [16 citations]
The following is the list of published articles that have cited the current article.
- R. Behzadi, E. Tohidi, and F. Toutounian, “Numerical Solution of Weakly Singular Fredholm Integral Equations Via Generalization of the Euler-Maclaurin summation Formula,” Journal of Taibah University for Science, 2013.
- 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.
- Emran Tohidi, F. Soleymani, and Adem Kilicman, “Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems,” Abstract And Applied Analysis, 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.
- 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.
- F. Toutounian, Emran Tohidi, and A. Kilicman, “Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications,” Abstract and Applied Analysis, vol. 2013, pp. 1–11, 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.
- Diana A. Bistrian, “A solution of the parabolized Navier–Stokes stability model in discrete space by two-directional differential quadrature and application to swirl intense flows,” Computers & Mathematics with Applications, 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.
- E. Tohidi, and A. Kılıçman, “An Efficient Spectral Approximation for Solving Several Types of Parabolic PDEs with Nonlocal Boundary Conditions,” Mathematical Problems in Engineering, vol. 2014, pp. 1–6, 2014.
- Ruiming Zhang, and Li-Chen Chen, “On Certain Matrices of Bernoulli Numbers,” Abstract and Applied Analysis, vol. 2014, pp. 1–4, 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.
- Emran Tohidi, “Application of Chebyshev collocation method for solving two classes of non-classical parabolic PDEs,” Ain Shams Engineering Journal, 2015.
- Anna Napoli, “Solutions of linear second order initial value problems by using Bernoulli polynomials,” Applied Numerical Mathematics, vol. 99, pp. 109–120, 2016.