IEEE Access (Jan 2019)

An Effective Algorithm for Delay Fractional Convection-Diffusion Wave Equation Based on Reversible Exponential Recovery Method

  • Tingyue Li,
  • Qifeng Zhang,
  • Wahidullah Niazi,
  • Yinghong Xu,
  • Maohua Ran

DOI
https://doi.org/10.1109/ACCESS.2018.2889735
Journal volume & issue
Vol. 7
pp. 5554 – 5563

Abstract

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In this paper, we investigate a linearized finite difference scheme for the variable coefficient semi-linear fractional convection-diffusion wave equation with delay. Based on reversible recovery technique, the original problems are transformed into an equivalent variable coefficient semi-linear fractional delay reaction-diffusion equation. Then, the temporal Caputo derivative is discreted by using $L_{1}$ approximation and the second-order spatial derivative is approximated by the centered finite difference scheme. The numerical solution can be obtained by an inverse exponential recovery method. By introducing a new weighted norm and applying discrete Gronwall inequality, the solvability, unconditionally stability, and convergence in the sense of $L_{2}$ - and $L_{\infty }$ - norms are proved rigorously. Finally, we present a numerical example to verify the effectiveness of our algorithm.

Keywords