In this study, numerical solution of generalized Rosenau–Kawahara equation with quintic B-spline collocation finite element method has been obtained. First, the generalized Rosenau–Kawahara equation is converted into a coupled differential equation system by the change of variable for the derivative with respect to space variable. Then, the numerical integrations of the resulting system according to time and space were obtained using the Crank–Nicolson-type formulation and quintic B-spline functions, respectively. The obtained numerical scheme has been applied to four model problems. It is seen that the results obtained from the presented scheme are compatible with the analytical solution, the error norms are smaller than those given in the literature, and conservation constants remain virtually unchanged.

本研究利用五次B样条搭配有限元方法得到广义Rosenau-Kawahara方程的数值解。首先，通过导数相对于空间变量的变量变化，将广义Rosenau-Kawahara方程转化为耦合微分方程组。然后，分别使用 Crank-Nicolson 型公式和五次 B 样条函数获得所得系统根据时间和空间的数值积分。所得数值方案已应用于四个模型问题。可以看出，从所提出的方案获得的结果与解析解兼容，误差范数小于文献中给出的误差范数，并且守恒常数几乎保持不变。