双曲方程初边值问题的高精度差分格式

A Difference Skeme of High Accuracy for Hyperbolic Inital Boundary Value Problem

双曲型方程?u/?t=a*(?u/?x)的差分格式 G.K.S.稳定的讨论已在给出,分别给出了两个截断误差为O(k^2+K^4)的格式,虽然计算时可取k～k^2,以便使格式有更好的精度,但此时时间步长k变得非常小,故原格式实际上只有二阶精度,本文中给出了一个具有G.K.S.

Centered difference approximation of fouth order both in space and time is applied to the mixed initial-boundary problem for hyperbolic equation. A method utilizing second order one-side difference at the boundary is showed to be stable and retain an overall third convergency order, finally, numerical example illustrate the success of the method for the problem.