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Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications

Author

Listed:
  • F. Toutounian
  • Emran Tohidi
  • A. Kilicman

Abstract

This paper introduces Fourier operational matrices of differentiation and transmission for solving high‐order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for generalized Pantograph equations with variable coefficients by using Legendre Gauss collocation nodes. In the case of numerical solution of Pantograph equation, an error problem is constructed by means of the residual function and this error problem is solved by using the mentioned collocation scheme. When the exact solution of the problem is not known, the absolute errors can be computed approximately by the numerical solution of the error problem. The reliability and efficiency of the presented approaches are demonstrated by several numerical examples, and also the results are compared with different methods.

Suggested Citation

  • F. Toutounian & Emran Tohidi & A. Kilicman, 2013. "Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:198926
    DOI: 10.1155/2013/198926
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    References listed on IDEAS

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    1. Faezeh Toutounian & Emran Tohidi & Stanford Shateyi, 2013. "A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, April.
    2. Faezeh Toutounian & Emran Tohidi & Stanford Shateyi, 2013. "A Collocation Method Based on the Bernoulli Operational Matrix for Solving High‐Order Linear Complex Differential Equations in a Rectangular Domain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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    Cited by:

    1. Emran Tohidi & M. M. Ezadkhah & S. Shateyi, 2014. "Numerical Solution of Nonlinear Fractional Volterra Integro‐Differential Equations via Bernoulli Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Emran Tohidi & Atena Pasban & A. Kilicman & S. Lotfi Noghabi, 2013. "An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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