Work

A new coupling algorithm for fractional diffusion equations based on multiscale functions

Year: 2025

Type: article

Abstract: We discuss a new discrete-continuous coupling algorithm for fractional diffusion equations based on piecewise interpolation polynomials and multiscale functions. This method considers to discretize the time fractional derivative using the L1-2 scheme while maintaining the continuity of the spatial variable. Then, the multiscale orthogonal polynomial algorithm is used to solve the spatial dimension equations, ultimately yielding the approximate solutions for the factional diffusion equations. Additionally, we provide the theoretical foundations of the algorithm and prove its convergence and stability. Through the test results of four examples, we validate the effectiveness and accuracy of the proposed approach.

Source: Alexandria Engineering Journal

DOI: 10.1016/j.aej.2025.02.041

Authors: Hui Zhu, Lei Yang, Ruimin Zhang, Yingchao Zhang, Yingzhen Lin

Institutions: Macau University of Science and Technology, Beijing Institute of Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,900

Funders: Science and Technology Development Fund, Department of Education of Guangdong Province