A Fractional Adams Method for Caputo Fractional Differential Equations with Modified Graded Meshes
Year: 2025
Type: article
Abstract: In this paper, we introduce an Adams-type predictor–corrector method based on a modified graded mesh for solving Caputo fractional differential equations. This method not only effectively handles the weak singularity near the initial point but also reduces errors associated with large intervals in traditional graded meshes. We prove the error estimates in detail for both 0<α<1 and 1<α<2 cases, where α is the order of the Caputo fractional derivative. Numerical experiments confirm the convergence of the proposed method and compare its performance with the traditional graded mesh approach.
Source: Mathematics
DOI: 10.3390/math13050891
Authors: Yuhui Yang, Yubin Yan
Institutions: Luliang University, University of Chester
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4408168920