Work

A fast second-order block-centered finite difference method for the fractional Cattaneo equation

Year: 2025

Type: article

Abstract: In this paper, a fast second-order block-centered finite difference method based on the $ \mathcal {FL} $2-$ 1_{\sigma} $ formula and a weighted approach was proposed for the time fractional Cattaneo equation. Using the special properties of the discrete coefficients and mathematical induction method, we derived the unconditional stability and convergence of the method rigorously. Second-order superconvergence in time and space for the velocity and pressure in discrete $ L^{\infty}(L^{2}) $-norms was established on non-uniform rectangular grids. Numerical examples were provided to verify our theoretical results.

Source: AIMS Mathematics

DOI: 10.3934/math.2025640

Author: Xianqiang Zhang

Institution: Ningxia University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: Natural Science Foundation of Ningxia Province