带色散的四阶抛物型方程的紧致差分格式  

Compact difference scheme for fourth-order parabolic equation with dispersion

作　　者：李冉冉 王红玉 开依沙尔·热合曼[1] LI Ranran;WANG Hongyu;KAYSAR Rahman(College of Mathematics and System Science,Xinjiang University,Urumqi 830046,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830046

出　　处：《山东科技大学学报（自然科学版）》2024年第1期82-88,共7页Journal of Shandong University of Science and Technology(Natural Science)

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

摘　　要：本研究提出一种有效求解带色散四阶抛物型方程的四阶紧致差分格式。对该方程的空间变量用四阶紧致差分格式进行离散,对离散之后得到的常微分方程组用三次Hermite插值法进行求解,得到一种空间和时间方向上都具有四阶精度的数值格式,并用傅里叶方法证明了该格式的无条件稳定性。数值实验中给出三种类型的算例,并将本研究格式与Crank-Nicolson格式进行数值比较,证明了本研究格式的有效性。结果表明,本研究格式对求解带色散的四阶抛物型方程具有很好的实用性。In this paper,a fourth-order compact difference scheme for efficiently solving the fourth-order parabolic equation with dispersion was proposed.The spatial variables of the equation were firstly discretized in the fourth-order compact difference scheme.The system of ordinary differential equations obtained after the discretization was then solved by the cubic Hermite interpolation method and a numerical scheme with fourth-order accuracy in both the spatial and temporal directions was obtained.The Fourier method was used to verify the unconditional stability of the scheme.Numerical experiments was conducted,in which three types of examples were given,and numerical comparisons was made between the proposed scheme and the Crank-Nicolson scheme,which verified the validity of the scheme.Numerical results show that the proposed scheme has good practicability in solving the fourth-order parabolic equations with dispersion.

关 键 词：带色散的四阶抛物型方程 紧致差分格式 三次Hermite插值 DIRICHLET边界条件 

分 类 号：O241.82[理学—计算数学]