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

作　　者：王红玉 李冉冉 开依沙尔·热合曼[1] WANG Hongyu;LI Ranran;RAHMAN Kaysar(College of Mathematics and System Science,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《安徽大学学报（自然科学版）》2024年第4期27-35,共9页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11461069);新疆大学博士启动基金资助项目(BS150204)。

摘　　要：针对1,2维带色散4阶扩散方程提出了一种高精度紧致格式.首先采用局部1维化方法将2维问题转化为x,y方向的两个1维带色散4阶扩散方程,其次分别对3,4阶空间导数进行6阶紧致格式离散,把带色散4阶扩散方程转化为一个常微分方程组,再利用求解常微分方程组的L-稳定的Simpson方法构造时间3阶、空间6阶精度的数值格式,并证明该格式是绝对稳定的.通过数值实验和比较,验证论文格式的有效性.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 

分 类 号：O241.82[理学—计算数学]