具弱色散误差的单调差分格式

本文基于1]、2]的理论分析,分别给出了计算(一维、二维)非线性双曲方程组的两类具弱色散误差的单调格式。§2针对一维气动力学方程组,通过数值结果。就激波的逼近问题,与已有的格式进行了比较。

Some Monotone Finite Difference Schemes with Weakly Dispersive Error

In this paper, we have given several schemes which have weakly dispersive error for the computation of the nonlinear hyperbolic equations in one and two dimensions. The construction of these schemes is based on the theoretical analysis of the papers1]and2].We have computed two model problems of the fluid dynamics in one dimension using Lax-Wendroff's scheme, MacCormack's scheme and the scheme provided in this paper. The numerical results show that our schemes have higher accuracy, and especially the oscilation is not appeared behind a shock.