Work

Numerical analysis and simulation of the compact difference scheme for the pseudo-parabolic Burgers' equation

Year: 2025

Type: article

Abstract: In this paper, we analyzed and tested a nonlinear implicit compact finite difference scheme for the pseudo-parabolic Burgers' equation. The discrete conservation laws and boundedness of the scheme were rigorously established. We then proved the unique solvability of the numerical scheme by reformulating it as an equivalent system. Furthermore, using the energy method, we derived an error estimate for the proposed scheme, achieving a convergence order of $ {\mathcal{O}}(\tau^2 + h^4) $ under the discrete $ L^\infty $-norm. The stability of the compact finite difference scheme was subsequently proven using a similar approach. Finally, a series of numerical experiments were performed to validate the theoretical findings.

Source: Electronic Research Archive

DOI: 10.3934/era.2025080

Authors: Yunxia Niu, Chaoran Qi, Yao Zhang, Wahidullah Niazi

Institutions: Xinjiang Institute of Technology, Zhejiang Sci-Tech University, Zhejiang Province Institute of Architectural Design and Research, Samangan Higher Education Institute

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,000

Funders: National Office for Philosophy and Social Sciences, Natural Science Foundation of Xinjiang