非线性SRLW方程的二重网格块中心有限差分方法

Two-Grid Block-Centered Finite Difference Method for Nonlinear Symmetric Regularized Long Wave Equations

本文研究求解非线性对称正则长波(SRLW)方程的二重网格块中心有限差分方法。二重网格法可以把非线性问题转化为在粗网格上求解小规模的非线性问题,在细网格上求解大规模的线性问题,使提高计算效率。块中心差分可同时高精度计算解及其导数。对时间采用Crank-Nicolson方法进行离散。数值实验结果显示,在均匀和非均匀网格上都是二阶收敛的。二重网格法的结果与完全非线性标准块中心差分格式的数值结果相比,在精度和效率上都具有优越性。

In this paper, a two-grid block-centered finite difference method for solving nonlinear symmetric regularized long wave(SRLW) equations is studied. The two-grid method can transform the nonlinear problem into a small-scale nonlinear problem on the coarse grid and a large-scale linear problem on the fine grid, so as to improve the computational efficiency. The block-centered difference can simultaneously calculate the solution and its derivatives with high accuracy. The time is discretiz by Crank-Nicolson method. The numerical results show that it is second-order convergent on both uniform and non-uniform meshes. The results of the two-grid method are superior to those of the fully nonlinear standard block-centered difference scheme in accuracy and efficiency.