标量双曲型守恒方程初边值问题的一种数值解法

A Kind of the Numerical Method for the Scalar Conservative Hyperbolic Equation

应用差分方法求双曲型守恒方程的数值解有很多缺点,例如:即使初值连续,也会产生不连续解.由此产生了激波及过超振荡现象.很多作者(LaxPD,HartenA,TadmorE,etal)都建立一些理论去处理它.但或多或少总还存在一些过超振荡现象,而且也不能应用于较长的时间层的计算.本文叙述了一种数值解法及其优点.克服了一些差分格式的缺点.也指出其不足之处,尚有待于进一步的探讨.

There are many defects in the numerical solution for the conservative hyperbolic equation of difference method. For example, even if the initialvalue of the problem is continuous , the discontinuity may occur also . Hence the phenomena of the shocks and overshock oscillation can not avoid to appear. A series of theorems has been established by some authors to avoid it, but above phenomena still exist more or less. Moreover, for the accumulation of the errors, the difference method can not be used for the calculation of the long time stage.In this paper, the advantages of the numerical (implicit) method are prescribed for the sake of the avoiding the disadvantages of the difference method. We also indicated the problems which are still open.