论文标题
本杰明 - 摩hon-burgers方程的线性化四阶保守紧凑型方案的均匀收敛和稳定性
Uniform convergence and stability of linearized fourth-order conservative compact scheme for Benjamin-Bona-Mahony-Burgers' equation
论文作者
论文摘要
在本文中，新开发的三分四阶紧凑型操作员用于为本杰明·巴诺 - 摩hon-Mahony-Burgers（BBMB）方程构建有效的紧凑型差异方案。详细的推导基于还原顺序方法以及三级线性化技术进行。详细研究了保守的，有限的和独特的解决性。统一的收敛是通过技术能源参数证明了最佳收敛顺序$ \ MATHCAL {O}（τ^2+H^4）$，从最大规范则表示。几乎无条件的稳定性可以根据数值解的均匀界限来实现。目前的方案在实用计算中非常有效，因为只有在每个时间步骤中需要求解具有对称循环矩阵的线性方程系统。广泛的数值示例验证了我们的理论结果，并证明了与参考文献中的最先进的方案相比，该方案的优越性。
In the paper, a newly developed three-point fourth-order compact operator is utilized to construct an efficient compact finite difference scheme for the Benjamin-Bona-Mahony-Burgers' (BBMB) equation. Detailed derivation is carried out based on the reduction order method together with a three-level linearized technique. The conservative invariant, boundedness and unique solvability are studied at length. The uniform convergence is proved by the technical energy argument with the optimal convergence order $\mathcal{O}(τ^2+h^4)$ in the sense of the maximum norm. The almost unconditional stability can be achieved based on the uniform boundedness of the numerical solution. The present scheme is very efficient in practical computation since only a system of linear equations with a symmetric circulant matrix needing to be solved at each time step. The extensive numerical examples verify our theoretical results and demonstrate the superiority of the scheme when compared with state-of-the-art those in the references.
