@article{Fu2026, 
author = {Yu Fu and Tian Gao and Yudie Hu and Zhifeng Weng},
title = {The High-Precision Scheme for the Coupled Burgers Equation},
year = {2026},
journal = {Journal of Xinjiang University(Natural Science Edition in Chinese and English)},
volume = {43},
number = {1},
pages = {27-37},
keywords = {coupled Burgers equation, barycentric interpolation collocation method, Crank-Nicolson, consistency analysis},
url = {https://www.sciopen.com/article/10.13568/j.cnki.651094.651316.2025.10.11.0001},
doi = {10.13568/j.cnki.651094.651316.2025.10.11.0001},
abstract = {This paper proposes the finite difference-barycentric interpolation collocation scheme for the nonlinearly coupled Burgers equation. For the coupled Burgers equation, it is firstly transformed into a linear equations via the direct linearization iteration. The spatial direction is discretized by the barycentric interpolation collocation method, and the time direction is discretized by the Crank-Nicolson scheme. The corresponding linear algebraic equations are derived. The consistency analysis is provided for the semi-discrete scheme in space and the fully discrete scheme. Numerical experiments verify the high precision and efficiency of our scheme.}
}