广义Rosenau-KdV方程的高精度守恒差分格式  

High-Order Conservative Finite Difference Scheme for the Generalized Rosenau-KdV Equation

作　　者：何育宇 王晓峰 邓雅清 HE Yu-yu;WANG Xiao-feng;DENG Ya-qing(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《数学的实践与认识》2023年第11期184-193,共10页Mathematics in Practice and Theory

基　　金：福建省中青年教师教育科研项目(JAT190368);福建省自然科学基金(2020J01796)。

摘　　要：对广义Rosenau-KdV方程提出一种在时间层和空间层上分别具有二阶和四阶精度的三层线性差分格式,所建格式是离散质量守恒和离散能量守恒的,利用离散能量法证明了差分格式的可解性、收敛性和稳定性.数值实验验证了该格式的精度和守恒性.A three-level linearized high-order conservative finite difference scheme for the generalized Rosenau-KdV equation is proposed.This scheme has second-and fourth-order accuracy in time and space respectively and is conservations of discrete mass and energy.Solvability,convergence and unconditional stability are proved by using the discrete energy method.Numerical experiments show that the proposed scheme has high accuracy and is conservative for discrete mass and energy.

关 键 词：广义Rosenau-KdV方程 高精度差分格式 守恒性 离散能量法 收敛性 

分 类 号：O241.3[理学—计算数学]