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High-order difference scheme for the solution of linear time fractional klein–gordon equations

Authors

  • Akbar Mohebbi,

    1. Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran
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  • Mostafa Abbaszadeh,

    1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 15914 Tehran, Iran
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  • Mehdi Dehghan

    Corresponding author
    1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 15914 Tehran, Iran
    • Correspondence to: Mehdi Dehghan; Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 15914 Tehran, Iran mdehghan@aut.ac.ir; mdehghan.aut@gmail.com

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Abstract

In this article, we apply a high-order difference scheme for the solution of some time fractional partial differential equations (PDEs). The time fractional Cattaneo equation and the linear time fractional Klein–Gordon and dissipative Klein–Gordon equations will be investigated. The time fractional derivative which has been described in the Caputo's sense is approximated by a scheme of order inline image, and the space derivative is discretized with a fourth-order compact procedure. We will prove the solvability of the proposed method by coefficient matrix property and the unconditional stability and inline image-convergence with the energy method. Numerical examples demonstrate the theoretical results and the high accuracy of the proposed scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1234–1253, 2014

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