奇异摄动问题在修正的Bakhvalov-Shishkin网格上的混合差分格式

The hybrid finite difference schemes on the modified Bakhvalov-Shishkin mesh for the singularly perturbed problem

在分3段修正的Bakhvalov-Shishkin网格上,将中点迎风格式和中心差分格式相结合,建立了新混合差分格式算法,以求解一维奇异摄动两点边值问题。借助截断误差、离散比较原理和障碍函数等,得到了与摄动参数ε一致的较好的收敛阶数,从粗网格部分到细网格部分依次为二阶收敛、一阶收敛和二阶收敛。数值算例表明,该方法在实际求解精度上较其他3种方法优越。

This paper develops a new hybrid finite difference scheme combining the midpoint upwind scheme with the central difference scheme on a three-piece modified Bakhvalov-Shishkin mesh to solve the singularly perturbed twopoint boundary value problem. Better ε-uniform accuracy and order of convergence are obtained by adopting truncation error, discrete comparison principle, barrier functions and so on. From the coarse mesh to the fine mesh, the error estimate of second-order convergence, first-order convergence and second-order convergence are obtained in turn. The numerical examples confirm the theoretical results and illustrate the advantage on accuracy of the method over the other three methods.