@Article{AAMM-16-1358,
author = {Peng , XiangyiQiu , WenlinWang , Jiangxing and Ma , Lina},
title = {A Novel Temporal Two-Grid Compact Finite Difference Scheme for the Viscous Burgers’ Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2024},
volume = {16},
number = {6},
pages = {1358--1380},
abstract = {<p style="text-align: justify;">We present a novel two-grid compact finite difference scheme for the viscous Burgers’ equation in this paper, where the second-order Crank-Nicolson method
is used to deal with the time marching, the compact finite difference formula is used to
approximate the spatial second-order term, and the nonlinear convection term is discretized using the developed nonlinear fourth-order operator, providing the scheme
with both high fourth-order spatial convergence and a low computational cost. The
scheme is then established in three steps, with the first step being the construction of a
nonlinear coarse-grid compact finite difference scheme that is solved iteratively using
a fixed point iterative method, the second step being the application of the Lagrange
interpolation formula to obtain a rough solution on the fine grid, and the third step being the development of the linearized fine-grid compact finite difference scheme. We
also perform a convergence and stability analysis on the developed scheme, and the
results show that the scheme can achieve spatial fourth-order and temporal second-order convergence. Finally, a number of numerical examples are provided to validate
the theoretical predictions.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0302},
url = {http://global-sci.org/intro/article_detail/aamm/23471.html}
}