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Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications

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  • 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, Hindawi, vol. 2013, pages 1-11, April.
    • Handle: RePEc:hin:jnlaaa:198926
    DOI: 10.1155/2013/198926
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    Cited by:

    1. Guimarães, O. & Labecca, W. & Piqueira, José Roberto C., 2020. "Generalized operational matrices and error bounds for polynomial basis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 258-272.

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