解方程■=f(x)的—族高稳定十字架格式

A CLASS OF CROSS-SCHEMES WITH HIGHER STABILITY PROPERTIES FOR ■=f(x)

建立了解二阶线性 Hamilton 方程的一族十字架格式,并把这些格式应用到波动方程中。如果选α=1/12,β=-1/48,那么就得到时间方向四阶精度格式,其稳定性条件比文献[2]中同类格式要好;当α=1/12,β=-1/30时,得到时间方向六阶精度格式,其稳定性条件要比文献[2]中时间方向为四阶精度格式要差。

A class of cross-schemes with two parameters α、β for linear Hamilton equa- tion of second order is established.These schemes are applied to wave equation.If α=(1/12), β=-(1/48),then four order accuracy schemes in time direction are obtained,their stability con- ditions will be better than the same kind schemes in Ref.[2].If α=(1/12),β=-(1/30),then six or- der accuracy schemes in time direction are obtained,their stability conditions will be worse than four order accuracy schemes in time direction in Ref.[2].