Camassa-Holm方程的两个局部能量守恒格式  

TWO LOCAL ENERGY-PRESERVING SCHEMES FOR THE CAMASSA-HOLM EQUATION

作　　者：张惠文 汪佳玲 Zhang Huiwen;Wang Jialing(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China;Center for Applied Mathematics of Jiangsu Province,Nanjing University of Information Science and Technology,Nanjing 210044,China;Jiangsu International Joint Laboratory on System Modeling and Data Analysis,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044 [2]南京信息工程大学江苏省应用数学中心,南京210044 [3]南京信息工程大学江苏省系统建模与数据分析国际合作联合实验室,南京210044

出　　处：《数值计算与计算机应用》2024年第3期249-261,共13页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11801277)资助。

摘　　要：本文为Camassa-Holm方程提出了两个局部能量守恒格式,不仅可以保持局部能量守恒还可以保持局部质量守恒,即在任何时空区域内能够精确保持能量和质量.局部能量守恒格式是全局能量守恒格式的推广,消除了(全局)保结构算法对边界条件的依赖.在合适的边界条件如周期边界条件或齐次边界条件下,局部能量守恒律和局部质量守恒律都可以转变为相应的全局守恒律.最后,数值实验验证了所提格式的良好性能。In this present work,we propose two local energy-preserving schemes for the Camassa-Holm equation,which can preserve both the local energy conservation law and the local mass conservation law,that is to say,these two schemes can accurately preserve energy and mass in any time and space regions.The local energy-preserving scheme is an extension of the global energy-preserving scheme,which eliminates the dependence on boundary conditions of the latter.Moreover,under suitable boundary conditions,such as periodic or homogeneous boundary condition,the local energy conservation law and local mass conservation law can be transformed into the corresponding global conservation laws.Finally,numerical experiments verify the splendid effect of the proposed schemes.

关 键 词：CAMASSA-HOLM方程 局部能量守恒格式 局部能量守恒律 局部质量守恒律 

分 类 号：O241.82[理学—计算数学]