Benjamin方程的高精度紧致有限差分法  

High-Order Compact Finite Difference Method for Benjamin Equation

作　　者：李晓芳 谢树森[1] LI Xiao-Fang;XIE Shu-Sen(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2018年第A02期193-197,共5页Periodical of Ocean University of China

基　　金：中央高校基本科研业务费专项(201562012);山东省自然科学基金项目(ZR2017MA016);国家重大科技专项(20101010)资助~~

摘　　要：本文提出一个解Benjamin方程的高精度显隐多步紧致有限差分格式,即在时间上对线性部分用三阶向后差分隐格式,非线性部分用显格式,空间上采用四阶精度紧致差分格式,最终在时间上和空间上分别达到三阶和四阶精度。证明了半离散紧致差分格式的四阶收敛性,给出了利用快速离散Fourier变换求解全离散格式的数值算法。最后数值算例验证了理论分析结果,并且数值解满足质量守恒定律。A high-orderimplicit-explicit multistep compact finite difference scheme is derived for the numerical solution of Benjamin equation.This scheme employs the third order backward difference method for the time discretization of linear part,while the explicit scheme for the nonlinear part.And for the space discretization,we use the forth order compact finite difference scheme.So we reach the third and the forth order accuracy in temporal and in spatial respectively.Convergence and error estimates are given for the semi-discrete compact scheme.With the fast Fourier transform,numerical results are presented to demonstrate the high-order accuracy and efficiency.Numerical results also show that the numerical solution of homogeneous Benjamin equation satisfies the conservation of mass.

关 键 词：BENJAMIN方程 HILBERT变换 紧致差分法 显隐多步向后差分法 

分 类 号：O241.82[理学—计算数学]