A Fractional Adams Method for Caputo Fractional Differential Equations with Modified Graded Meshes

Yuhui Yang and Yubin Yan ()
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Yuhui Yang: Department of Mathematics and Artificial Intelligence, Lyuliang University, Lishi, Lüliang 033000, China
Yubin Yan: School of Computer and Engineering Sciences, University of Chester, Chester CH1 4BJ, UK

Mathematics, 2025, vol. 13, issue 5, 1-34

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.

Keywords: fractional Adams method; Caputo fractional derivative; modified graded mesh; nonlinear fractional differential equations; numerical methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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