对称正则长波方程的高效紧致差分格式  

An Efficient Compact Difference Scheme for the Symmetric Regularized Long Wave Equation

作　　者：高晶英 何斯日古楞 青梅 额尔敦布和 GAO Jingying;HE Siriguleng;QING Mei;Eerdunbuhe(School of Mathematics and Big Data,Hohhot Minzu College,Hohhot 010051,P.R.China)

机构地区：[1]呼和浩特民族学院数学与大数据学院,呼和浩特010051

出　　处：《应用数学和力学》2025年第3期412-424,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12161034)。

摘　　要：为了求出对称正则长波(symmetric regularized long wave,SRLW)方程的数值解,构造了一种新的高效紧致有限差分格式.采用经典的Crank-Nicolson(C-N)格式和外推技术对时间方向一阶导数进行离散化,使用四阶Padé方法和逆紧致算子分别对空间方向一阶和二阶导数进行离散化,使得构造的格式具有线性、非耦合和紧致的特点,极大地提高了求解效率.此外,还对新格式进行了守恒律、先验估计、稳定性、收敛性分析,证明了其在时间上达到二阶、在空间上达到四阶收敛精度.最后,通过一个数值算例验证了理论的正确性和格式的高效性.A new efficient and compact finite difference scheme was constructed to obtain numerical solutions of the symmetric regularized long wave equation.The classic Crank-Nicolson(C-N)scheme and the extrapolation technique were used for discretization of the 1st-order derivatives in the temporal direction,the 4th-order Padémethod and the inverse compact operator were applied for discretization of the 1st-order and 2nd-order derivatives in the spatial direction,respectively.The constructed scheme has the linear,uncoupled,and compact features,greatly enhancing the computational efficiency.Additionally,analyses on conservation laws,a priori estimates,stability and convergence were conducted for the new scheme,to prove the 2nd-order temporal and the 4th-order spatial convergence accuracies.Finally,the theoretical correctness and efficiency of the scheme were verified through a numerical example.

关 键 词：对称正则长波方程 有限差分 高效 紧致 

分 类 号：O241.82[理学—计算数学]