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Numerical solution of time fractional nonlinear Klein–Gordon equation using Sinc–Chebyshev collocation method

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  • Nagy, A.M.

Abstract

In this paper, we proposed a new numerical scheme to solve the time fractional nonlinear Klein–Gordon equation. The fractional derivative is described in the Caputo sense. The method consists of expanding the required approximate solution as the elements of Sinc functions along the space direction and shifted Chebyshev polynomials of the second kind for the time variable. The proposed scheme reduces the solution of the main problem to the solution of a system of nonlinear algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces accurate results.

Suggested Citation

  • Nagy, A.M., 2017. "Numerical solution of time fractional nonlinear Klein–Gordon equation using Sinc–Chebyshev collocation method," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 139-148.
    • Handle: RePEc:eee:apmaco:v:310:y:2017:i:c:p:139-148
    DOI: 10.1016/j.amc.2017.04.021
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    References listed on IDEAS

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    1. Sun, HongGuang & Chen, Wen & Li, Changpin & Chen, YangQuan, 2010. "Fractional differential models for anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2719-2724.
    2. Sweilam, N.H. & Nagy, A.M. & El-Sayed, Adel A., 2015. "Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 141-147.
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    Cited by:

    1. Huang, Qiong-Ao & Zhang, Gengen & Wu, Bing, 2022. "Fully-discrete energy-preserving scheme for the space-fractional Klein–Gordon equation via Lagrange multiplier type scalar auxiliary variable approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 265-277.
    2. H. Çerdik Yaslan, 2021. "Numerical solution of the nonlinear conformable space–time fractional partial differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 407-419, June.

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