RLW-KdV方程的一个高精度非线性守恒C-N差分格式  

A High-order Nonlinear Conserved C-N Differential Scheme for the RLW-KdV Equation

作　　者：胡俊林 吴明明 胡劲松 HU Junlin;WU Mingming;HU Jinsong(School of Science,Xihua University,Chengdu 610039 China)

机构地区：[1]西华大学理学院,四川成都610039

出　　处：《西华大学学报(自然科学版)》2025年第3期107-112,共6页Journal of Xihua University:Natural Science Edition

基　　金：国家自然科学基金青年基金项目(11701481);四川应用基础研究项目(2019JY0387)。

摘　　要：对RLW-KdV方程的初边值问题提出一个新的高精度非线性守恒差分算法。利用Taylor展开,在空间层做部分外推处理,直接从整体上抵消空间截断误差的二阶部分,在时间层采用Crank-Nicolson格式,从而在时间方向和空间方向分别达到了二阶精度和四阶精度,并合理地模拟了问题本身的一个守恒量,利用离散Sobolev嵌入不等式和离散泛函分析方法,证明了格式的收敛性和稳定性。数值算例验证了该方法是可行的。A new high-order nonlinear conservative difference scheme was proposed for the initial boundary value problems of the RLW equation.The Taylor expansion and the partial extrapolation were used to make the second-order term of the truncation error be removed directly at the spatial layer,and the Crank-Nicolson scheme was adopted at the temporal layer,which results in second-order and fourth-order ac-curacy in the temporal and spatial directions,respectively,and reasonably simulates a conserved quant-ity of the problem itself.The convergence and stability of this scheme were proved by discrete Sobolev em-bedding inequality and the discrete functional analysis method,and the results of the numerical example ex-periments verify that the method is feasible.

关 键 词：RLW-KdV方程 高精度 守恒 差分格式 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]