Electron. J. Differential Equations, Vol. 2026 (2026), No. 32, pp. 1-14.

Linearized high-order and convergent scheme for the Kuramoto-Sivashinsky equation

Yiran Zhang, Guohui Wang, Yuanfeng Jin

Abstract:
In this article, we provide a linearized compact scheme for the Kuramoto-Sivashinsky equation with the periodic boundary condition. By applying the double reduction order method and a fourth-order compact operator, the scheme achieves second-order convergence in time and fourth-order convergence in space. We present proofs of the conservation, unique solvability, and convergence of the scheme.

Submitted November 19, 2025. Published April 30, 2026.
Math Subject Classifications: 65M06, 65M12.
Key Words: Kuramoto-Sivashinsky equation; linearized compact scheme; reduction order method; conservation law; convergence.
DOI: 10.58997/ejde.2026.32

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Yiran Zhang
College of Science
Yanbian University
Yanji 133002, China
email: 3157889605@qq.com
Guohui Wang
College of Science
Yanbian University
Yanji 133002, China
email: 1547733468@qq.com
Yuanfeng Jin
College of Science
Yanbian University
Yanji 133002, China
email: yfkim@ybu.edu.cn

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