A block‐centered finite difference method for fractional Cattaneo equation

Abstract

In this article, a block-centered finite difference method for fractional Cattaneo equation is introduced and analyzed.The unconditional stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete L 2 norm with optimal order of convergenceboth for pressure and velocity are established on nonuniform rectangular grids. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

A Fast Compact Block-Centered Finite Difference Method on Graded Meshes for Time-Fractional Reaction-Diffusion Equations and Its Robust Analysis

“…For comparison, we also test the second-order in space fast L1-BCFD method for model (1.1) (4.4). This scheme can be derived similarly as [51] for the time-fractional diffusion equation or [23] for the time-fractional Cattaneo equation.…”

“…Besides, the BCFD method can guarantee the mass conservation and result in a symmetric positive definite system, compared with a saddle-point system generated by the classical mixed element method [34]. Therefore, the BCFD method is more efficient and widely used for modeling of flow model [37,58], convection-diffusion model [52], and even time-fractional model [17,22,23,51]. Recently, Shi et al [40] proposed a compact BCFD method for the elliptic and parabolic problems, which further improves the spatial accuracy from second-order to fourth-order.…”

“…Recently, Shi et al [40] proposed a compact BCFD method for the elliptic and parabolic problems, which further improves the spatial accuracy from second-order to fourth-order. However, the analysis in [40] cannot be directly applied to the time-fractional reaction-diffusion equation (1.1), and up to now, there are indeed no work on high-order BCFD method for model (1.1), and error analysis of most available second-order BCFD methods [22,23,51] are based upon smoothness assumption of the solution.…”

Comparative Numerical Study of Spline-Based Numerical Techniques for Time Fractional Cattaneo Equation in the Sense of Caputo–Fabrizio

“…Caputo and Fabrizio proposed one of the most recent fractional order derivatives. For more applications of this new derivative and the related work, the reader is referred to [1,[16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”