Cahn-Hilliard方程的一个超紧致有限差分格式  

A supercompact finite difference scheme for Cahn-Hilliard equations

作　　者：栗雪娟[1] 王丹 LI Xuejuan;WANG Dan(School of Science,Xi′an University of Architecture and Technology,Xi′an 710055,China)

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《山东理工大学学报（自然科学版）》2024年第1期73-78,共6页Journal of Shandong University of Technology:Natural Science Edition

基　　金：陕西省自然科学基金项目(2018JQ1043)。

摘　　要：研究四阶Cahn-Hilliard方程的数值求解方法。给出组合型超紧致差分格式,将其用于四阶Cahn-Hilliard方程的空间导数离散,采用四阶Runge-Kutta格式离散时间导数,将二者结合得到四阶Cahn-Hilliard方程的离散格式,并给出了该格式的误差估计。通过编程计算得到其数值解,并与精确解进行对比,结果表明本文的数值方法误差小,验证了所提方法的有效性和可行性。A numerical method for solving the fourth order Cahn-Hilliard equation is studied.The combinational ultra-compact difference scheme is given and applied to the spatial derivative discretization of the fourth order Cahn-Hilliard equation.The fourth-order Runge-Kutta scheme is used to discrete time derivatives.The discrete scheme of the fourth order Cahn-Hilliard equation is obtained by combining the two methods,and the error estimate of the scheme is given.Finally,the numerical solution is obtained by programming and compared with the exact solution.The results show that the numerical method in this paper has a small error,verifying the effectiveness and feasibility of the proposed method.

关 键 词：四阶Cahn-Hilliard方程 组合型超紧致差分方法 四阶Runge-Kutta方法 误差估计 

分 类 号：TB532.1[理学—物理] TB553[理学—声学]