应用数学和力学2026，Vol.47Issue(9)：1197-1210,14.DOI:10.21656/1000-0887.470066
基于广义梯形公式的二维Burgers方程三阶数值解法
A 3rd-Order Numerical Method for 2D Burgers Equations Based on the Generalized Trapezoid Formula
摘要
Abstract
The Burgers equation has been widely applied in many fields such as fluid mechanics due to its accu-rate description of nonlinear transport and dissipation mechanisms.A numerical method for a class of 2D non-linear Burgers equations was studied.Firstly,the Burgers equation was transformed into a class of heat conduc-tion equations via the Hopf-Cole transformation.Then,the high-order barycentric rational spectral approxima-tion was used in the spatial direction to obtain the semi-discrete scheme,and the generalized trapezoidal formu-la with parameterδwas adopted in the temporal direction,thus to obtain the fully discrete scheme for the trans-formed equation.For parameter δ=1/3,the truncation error in the temporal direction has 3rd-order accuracy.Finally,numerical examples verify the correctness of the truncation error analysis.关键词
Burgers方程/Hopf-Cole/高阶重心有理插值配置法/广义梯形公式Key words
Burgers equation/Hopf-Cole/high-order barycentric rational interpolation collocation method/generalized trapezoidal formula分类
数理科学引用本文复制引用
刘陶,刘利斌..基于广义梯形公式的二维Burgers方程三阶数值解法[J].应用数学和力学,2026,47(9):1197-1210,14.基金项目
国家自然科学基金(12361087) （12361087）
广西自然科学基金(2025GXNSFAA069738) （2025GXNSFAA069738）
