一维Zakharov-Rubenchik方程的有效紧致差分格式  

EFFICIENT COMPACT FINITE DIFFERENT SCHEME FOR THE ONE-DIMENSIONAL ZAKHAROV-RUBENCHIK EQUATIONS

作　　者：胡云霞 李宏伟 Hu Yunxia;Li Hongwei(School of Mathematics and Statistics,Shandong Normal University,250358,Jinan,China)

机构地区：[1]山东师范大学数学与统计学院,济南250358

出　　处：《山东师范大学学报（自然科学版）》2020年第2期149-157,共9页Journal of Shandong Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11401350);山东省自然科学基金资助项目(ZR2019BA002).

摘　　要：偏微分方程的有限差分法是科学计算中的一种有效方法,采用经典的一阶和二阶有限差分格式对方程进行数值求解,要想得到较高精度的近似解是不容易的,一种合理的方法是设计高阶紧致差分格式.为了研究一维Zakharov-Rubenchik方程的有效紧致差分格式及其数值计算.针对一般形式的Zakharov-Rubenchik方程,提出了一种半隐式紧致有限差分格式,该格式克服了传统差分格式效率低、精确度不足的缺点,并在离散层次上保持了质量和能量的守恒性.最后,通过数值算例验证了该格式的精确程度及守恒性,并对几种不同差分格式的误差和计算耗时进行了比较,数值结果表明了半隐式紧致差分格式的高阶收敛性及有效性.Finite difference method of partial differential equation is an effective method in scientific calculation.It is not easy to obtain the numerical solution with high accuracy by using the classical first-order and second-order finite difference schemes.A reasonable method is to design the high-order compact difference scheme.An efficient compact finite difference scheme to numerically solve the one-dimensional Zakharov-Rubenchik equations is proposed in this paper.We develop a semi-implicit compact finite difference scheme that conserves the mass and the energy in the discrete level for the Zakharov-Rubenchik equations.Then,some numerical examples are given to demonstrate the accuracy,conservation and effectiveness of the proposed scheme,and the comparison of difference schemes in the errors and time-consuming is carried out to illustrate the efficiency of semi-implicit compact finite difference scheme.

关 键 词：Zakharov-Rubenchik方程 紧致有限差分格式 离散守恒定律 

分 类 号：O241.82[理学—计算数学]