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Space-time spectral method for the Cattaneo equation with time fractional derivative

Author

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  • Li, Hui
  • Jiang, Wei
  • Li, Wenya

Abstract

This paper introduces a high-order accurate numerical method for solving the Cattaneo equation with time fractional derivative. It is based on the Galerkin–Legendre spectral method in space and the Chebyshev collocation method in time. Arbitrarily high-order accurate can be made in both space and time. Optimal priori error bound of the semi-discrete method and the stability and convergence of the full-discrete method are strictly given. Extensive experimental results confirm the theoretical claims of this method in both space and time.

Suggested Citation

  • Li, Hui & Jiang, Wei & Li, Wenya, 2019. "Space-time spectral method for the Cattaneo equation with time fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 325-336.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:325-336
    DOI: 10.1016/j.amc.2018.12.050
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    References listed on IDEAS

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    1. Alvarez-Ramirez, Jose & Fernandez-Anaya, Guillermo & Valdes-Parada, Francisco J. & Alberto Ochoa-Tapia, J., 2006. "A high-order extension for the Cattaneo's diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 345-354.
    2. Ran, Yu-Hong & Wang, Jun-Gang & Wang, Dong-Ling, 2015. "On HSS-like iteration method for the space fractional coupled nonlinear Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 482-488.
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    1. Fernandez-Anaya, G. & Valdes-Parada, F.J. & Alvarez-Ramirez, J., 2011. "On generalized fractional Cattaneo’s equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4198-4202.

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