Work

Sinc-Galerkin method and a higher-order method for a 1D and 2D time-fractional diffusion equations

Year: 2024

Type: article

Abstract: In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference formula is considered for temporal discretization. The convergence behavior of the methods is analyzed, and the error bounds are provided. The main objective of this paper is to propose the error bounds for 2D problems by using the Sinc-Galerkin method. The proposed method in terms of convergence is studied by using the characteristics of the Sinc function in detail with optimal rates of exponential convergence for 2D problems. Some numerical experiments validate the theoretical results and present the efficiency of the proposed schemes.

Source: Boundary Value Problems

DOI: 10.1186/s13661-024-01915-6

Authors: Man Luo, Da Xu, Xianmin Pan

Institutions: Hunan Women'S University, Hunan Normal University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,790

Funders: Education Department of Hunan Province, Scientific Research Foundation of Hunan Provincial Education Department