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

oleh: Tingyue Li, Qifeng Zhang, Wahidullah Niazi, Yinghong Xu, Maohua Ran

Format: Article
Diterbitkan: IEEE 2019-01-01

Deskripsi

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 <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula>- and <inline-formula> <tex-math notation="LaTeX">$L_{\infty }$ </tex-math></inline-formula>- norms are proved rigorously. Finally, we present a numerical example to verify the effectiveness of our algorithm.