Group preserving schemes for nonlinear dynamic system based on RKMK methods

A survey of the precise integration method

“…空间的 Lie 群型动力系统 [80,81] , [88,89] 、矩阵微分 Riccati 方程求解 [11] 、卡尔曼-布西滤波 [90] 、 H  控制系统的 分析与设计 [91,92] 等方面得到应用, 这方面的详细情 况可参考文献 [93,94]. 目前, 两点边值问题的精细积 分方法已在分层介质中波传播问题 [95~98] 、表面波问 题 [99,100] [109] , 奇异摄动边 值问题 [110] 等方面得到了广泛的应用.…”

The Lie-group method based on radial basis functions for solving nonlinear high dimensional generalized Benjamin–Bona–Mahony–Burgers equation in arbitrary domains

“…From the class of numerical Lie group methods, the so-called group preserving scheme (GPS), introduced by Liu [20], is a numerical approach which utilizes the Cayley transformation and the Padé approximations in the Minkowski space. Avoiding the spurious solutions and ghost fixed points are main benefits of this method [21][22][23][24][25][26].…”