Work

Error Analysis of the L1 Scheme on a Modified Graded Mesh for a Caputo–Hadamard Fractional Diffusion Equation

Year: 2025

Type: article

Abstract: The L1 scheme on a modified graded mesh is proposed to solve a Caputo–Hadamard fractional diffusion equation with order α∈(0,1). Firstly, an improved graded mesh frame is innovatively constructed, and its mathematical properties are verified. Subsequently, a new truncation error bound for the L1 discretisation format of Caputo–Hadamard fractional-order derivatives is established by means of a Taylor cosine expansion of the integral form, and a second-order central difference method is used to achieve high-precision discretisation of spatial derivatives. Furthermore, a rigorous analysis of stability and convergence under the maximum norm is conducted, with special attention devoted to validating that the L1 approximation scheme manifests an optimal convergence order of 2−α when deployed on the modified graded mesh. Finally, the theoretical results are substantiated through a series of numerical experiments, which validate their accuracy and applicability.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9050286

Authors: Dan Liu, Libin Liu, Hongbin Chen, Xiongfa Mai

Institutions: Nanning Normal University, Central South University of Forestry and Technology

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: National Natural Science Foundation of China, Natural Science Foundation of Guangxi Province, Division of Graduate Education