对双曲型方程两种差分格式方法的比较研究

A Comparative Study of Two Difference Schemes for Hyperbolic Equations

摘要: 显式和隐式差分格式法是求解双曲型偏微分方程的两种常用方法。通过应用这两种方法计算二阶双曲型偏微分方程的数值解和误差，以及分析其程序运行时间，本文对其进行了深刻比较。结果发现：显式差分格式法计算简单，程序运行时间短，但是，当选取的步长比比较小的时候，显示差分格式法的算法不收敛；而隐式差分格式法，对任意的步长比都收敛，但是，其计算过程比较复杂，且程序运行时间较长。

Abstract: Explicit and implicit difference schemes are two common methods for solving hyperbolic partial differential equations. By using these two methods to calculate the numerical solution and error of the second order hyperbolic partial differential equation, and analyzing the program running time, this paper makes a deep comparison between them. The results show that: the explicit difference scheme method is simple in calculation and its program running time is short, but when the se-lected step ratio is small, it shows that the algorithm of the explicit difference scheme method is not convergent; while the implicit difference scheme method is convergent for any step ratio, but its calculation process is more complex and the program running time is longer.