求解一维对流方程的高精度紧致差分格式

本文提出数值求解一维对流方程的一种两层隐式紧致差分格式,采用泰勒级数展开法以及对截断误差余项中的三阶导数进行修正的方法对时间和空间导数进行离散.格式的截断误差为O(τ^4 +τ^2h^2 + h^4),即该格式在时间和空间上均可达到四阶精度.利用von Neumann方法分析得到该格式是无条件稳定的.通过数值实验验证了本文格式的精确性和稳定性.

A High-Order Compact Difference Scheme for Solving the 1D Convection Equation

In this paper, a two-level implicit compact difference scheme for solving the onedimensional convection equation is proposed. Taylor series expansion and correction for the third derivative in the truncation error remainder of the central difference scheme are used for the discretization of time and space. The local truncation error of the scheme is O(τ^4 + τ^2h^2 + h^4),i.e., it has the fourth-order accuracy in both time and space. The unconditional stability is obtained by the von Neumann method. The accuracy and the stability of the present scheme are validated by some numerical experiments.