Work

A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular Solution

Year: 2025

Type: article

Abstract: In this paper, we establish a fast Crank-Nicholson L1 finite difference formula for two-dimensional fractional mobile/immobile diffusion equations with weakly singular solutions at the initial moment. First, the time fractional derivative is discretized by the Crank-Nicolson formula on uniform meshes, and the spatial derivative is discretized by the central difference quotient formula on uniform meshes. A numerical scheme is established, and local truncation error estimate is given. Then, the Von-Neumann stability analysis method is used to analyze the stability of the scheme, and the optimal error estimates are given by Fourier analysis and energy analysis methods, respectively. On the other hand, we optimize the numerical format based on the sum-of exponentials approximation (SOE), which effectively reduces the amount of computation and memory. Finally, numerical examples verify the effectiveness of the scheme and theoretical analysis.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9040204

Authors: Haili Qiao, Aijie Cheng

Institutions: Liaocheng University, Shandong University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funders: Liaocheng University, Natural Science Foundation of Shandong Province