Work

The ADI difference and extrapolation scheme for high-dimensional variable coefficient evolution equations

Year: 2025

Type: article

Abstract: This paper investigated a numerical method for a two-dimensional variable coefficient evolution equation (VCEE), utilizing the alternating direction implicit (ADI) method and an extrapolation formula. The time derivative was discretised by the backward Euler (BE) scheme on a uniform mesh and the finite difference method (FDM) was applied to spatial discretization. We proved an priori estimate and the error bound of the solution to the difference scheme using the energy analysis method, and verified the uniqueness, stability, and convergence of the proposed scheme. To further improve numerical accuracy, we introduced a Richardson extrapolation method, which enhances the global accuracy to fourth order. Finally, some numerical examples were provided to demonstrate the validity of the theoretical analysis.

Source: Electronic Research Archive

DOI: 10.3934/era.2025146

Authors: Jinxiu Zhang, Xuehua Yang, Song Wang

Institutions: Hunan University of Technology, Curtin University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,000

Funders: National Natural Science Foundation of China, Natural Science Foundation of Hunan Province