安徽大学学报（自然科学版）2024，Vol.48Issue(4)：27-35,9.DOI:10.3969/j.issn.1000-2162.2024.04.005
2维带色散4阶扩散方程的高精度紧致格式
High order compact scheme for the two-dimensional fourth-order diffusion equations with dispersion
摘要
Abstract
In this paper,a high-order compact scheme for one-dimensional and two-dimensional fourth-order diffusion equation with dispersion was proposed.Firstly,the two-dimensional problem was transformed into two one-dimensional fourth-order diffusion equations with dispersion in the x and y directions by using the local one-dimensional method.Secondly,the third-order and fourth-order spatial derivatives were discretized by the sixth-order compact scheme respectively,and the fourth-order diffusion equation with dispersion was transformed into a system of ordinary differential equations,then the L-stable Simpson method for solving ordinary differential equations was used to construct the numerical scheme with third-order accuracy in time and sixth-order accuracy in space,and it was proved that the scheme was absolutely stable.Numerical experiments and comparisons verified the effectiveness of the proposed scheme.关键词
2维带色散4阶扩散方程/高精度紧致差分格式/Crank-Nicolson格式/局部1维化方法/L-稳定Simpson格式Key words
two-dimensional fourth-order diffusion equation with dispersion/high-order compact difference scheme/Crank-Nicolson scheme/local one-dimensional method/L-stable Simpson scheme分类
数理科学引用本文复制引用
王红玉,李冉冉,开依沙尔·热合曼..2维带色散4阶扩散方程的高精度紧致格式[J].安徽大学学报（自然科学版）,2024,48(4):27-35,9.基金项目
国家自然科学基金资助项目(11461069) （11461069）
新疆大学博士启动基金资助项目(BS150204) （BS150204）
