High-order rotated grid point iterative method for solving 2D time fractional telegraph equation and its convergence analysis

Computational and Applied Mathematics volume 40, Article number: 54 (2021) Cite this article

Abstract

In this paper, the compact finite difference (CFD) and rotated four-point compact explicit decoupled group (CEDG) methods are proposed to solve the two-dimensional time-fractional telegraph equation. The CEDG method is derived from a rotated of CFD approximation formula combine with the arranging of the grid points in the form of a group. This method shows superior performance in the term of CPU timings and iteration compared to the CFD method on the standard grid but with the same order of accuracy. We have proved the stability and convergence of the proposed schemes using the Fourier analysis. The convergence order of the proposed methods is \(O\left( \tau +h_{x}^{4}+h_{y}^{4}\right) \). Some numerical experiments are performed to demonstrate the effectiveness of the proposed methods.

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Acknowledgements

We are very grateful to anonymous referees for their careful reading and valuable comments which led to the improvement of this paper. The authors are also very grateful to the Associate Editor, Professor Vasily E. Tarasov for managing the review process.

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Affiliations

  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, 41938, Iran

    N. Abdi & H. Aminikhah

  2. Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, P.O. Box 1914, Rasht, 41938, Iran

    H. Aminikhah

  3. Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran

    A. H. Refahi Sheikhani

Authors
  1. N. Abdi
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  2. H. Aminikhah
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  3. A. H. Refahi Sheikhani
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Correspondence to H. Aminikhah.

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Communicated by Vasily E. Tarasov.

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Abdi, N., Aminikhah, H. & Sheikhani, A.H.R. High-order rotated grid point iterative method for solving 2D time fractional telegraph equation and its convergence analysis. Comp. Appl. Math. 40, 54 (2021). https://doi.org/10.1007/s40314-021-01451-4

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Keywords

  • Crank–Nicolson method
  • Compact scheme
  • Rotated finite difference
  • Explicit decoupled group method
  • Caputo fractional derivative
  • Stability
  • Convergence

Mathematics Subject Classification

  • 34K37
  • 65M06
  • 65D07